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Stochastic fuzzy analysis and its applications

Research Project

Project/Area Number 09440085
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionSaga University

Principal Investigator

OGURA Yukio  Saga University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (00037847)

Co-Investigator(Kenkyū-buntansha) SUGITA Hiroshi  Kyushu University, Graduate School of Mathematics, Associate Professor, 大学院・数理学研究科, 助教授 (50192125)
NAGAI Hideo  Osaka University, Graduate School of Fundamental Engineering, Professor, 基礎工学部, 教授 (70110848)
KUSUOKA Shigeo  University of Tokyo, Graduate School of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (00114463)
LI Shoumei  Saga University, Faculty of Science and Engineering, Associate Professor, 理工学部, 助教授 (00304874)
MITOMA Itaru  Saga University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (40112289)
三苫 至  佐賀大学, 理工学部, 教授 (09640279)
半田 賢司  佐賀大学, 理工学部, 助教授 (10238214)
Project Period (FY) 1997 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥8,300,000 (Direct Cost: ¥8,300,000)
Fiscal Year 1999: ¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1998: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1997: ¥3,000,000 (Direct Cost: ¥3,000,000)
Keywordsfuzzy analysis / fuzzy martingale / random set / random fuzzy set / graph onvergence / separability for convergence / law of large numbers / optional stopping theorem / デファジィフィケイション / ファジィマルチシゲール / ファジィマルチンゲ-ル / Kudo-Aumann積分 / 優マルチンゲ-ル / 劣マルチンゲ-ル
Research Abstract

Former study on limit theorems for random fuzzy sets was mainly for the case of compact level sets. This is due to its method which is based on the embedding theorem of convex compact sets into the space of bounded continuous functions on the unit closed ball in the dual space. The object of this project is to obtain limit theorems for wider class of random fuzzy sets, extending the former study.
There are two cases where the compactness condition fails. One is the case of bounded but non compact sets, which occurs in infinite dimension cases. The other is that of unbounded sets, which occurs even in finite dimensional cases. In the former case, the first problem one may encounter is the closedness of the Aumann integrals. This integral is fundamental in the study of random sets or random fuzzy sets, and although a counter example for the closeness was known, a good sufficient condition was not known. In this project, we obtained that the Aumann integral is closed if the underlying spac … More e is a reflexive Banach space. We next dealt with the concept of convergence, which is significant in both former and latter cases. In most of former works, the fuzzy sets were treated as simple collections of level sets and the topologies sometimes differs from intuition. In this project, we introduced a new concept called graph convergence which fits intuition more, and improved various convergence theorems. Finally, we also obtained separability theorem for graph convergence, which ensures that one have only to check the convergence of level sets for countably many levels for a proof of convergence of random fuzzy sets.
Based on the former theoretical advance, we obtained or improved various limit theorems on random sets and/or random fuzzy sets, which covers law of large numbers, limit theorems for martingale and s-martingales, regular representation theorem for martingales, optional sampling theorems, approximation of random fuzzy sets and representation theorem of Gaussian random fuzzy sets. Less

Report

(4 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report
  • Research Products

    (115 results)

All Other

All Publications (115 results)

  • [Publications] S. Li: "An optional samplimg theorem for fuzzy valued martingales"Seventh International fuzzy Systems Association World Congress. IV. 9-14 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A. kasue: "Convergence of heat kernels on a compact manifold"Kyushu J. Math.. 51. 453-524 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Li: "Convergence of set valued sub- and super-martingales in the Kuratowski-Mosco sense"Ann. Prob.. 26. 1384-1402 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 小倉幸雄: "確率ファジィ解析-「確率ファジィ解析とその周辺」特集にあたって-"日本ファジィ学会誌. 10. 2-9 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Li: "Convergence of set valued and fuzzy valued martingales and smartingales in the Kuratowski-Mosco sense"Proceedings Seventh International Conference IPMU. 72-79 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Li: "Convergence theorems for set valued and fuzzy valued martingales and smartingales"Jour. Korean Math. Soc.. 33. 765-782 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Ogura: "Superposition of diffusion processes - Feller property -"Trends in probability and Related Analysis, eds. Kono, N. & N. R. Sieh. 113-128 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Li: "Convergence of set-valued abd fuzzy-valued martingales"Fuzzy seys and systems. 101. 453-461 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Li: "Anapproximation theorem for unbounded fuzzy valued random variables"Proceedings of the Eighth International Fuzzy Systems Association world Congress. 2. 1042-1046 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Li: "Fuzzy Gaussian processes and martimgale with continuous parameter"Proceedings of the Fifth Joint Conference on Information Sciences. 1. 146-149 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Li: "Convergence in graph for fuzzy valued martingales and smartingale"Statistical Modeling, Analysis and Management of Fuzzy Data eds. M. A. Gil, Bertoluzza and D.A. Ralescu. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Ogura: "Set defuzzification and Choquet integral"International Journal of uncertainty, Fuzziness and Knowledge-based Systems. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Ogura: "Existence of strong solution for an integro-differential equation and superposition of diffusion processes"Stochastics in Finite/infinite Dimensions 8In honor of Gopinath Kallianpur). (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N. Ikeda: "Short time asymptotics for fundamental solutions of heat equations with boundary conditions"New Trends in Stochastic Analysis ed. K. D. Elworthy, S. Kusuoka and I. Shigekawa, World Scientific Pub.. 182-219 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Kusuoka: "Waves on fractal-like manifolds and effective energy propagation"Prob. Ther. And Rel. Fields. 110. 473-495 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Kusuoka: "A remark on default risk models"Advances in mathmatical Economics eds. S. Kusuoka, m. Maruyama. vol. 1. 69-82 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Kusuoka: "Term Structure and SPDE"Advances in mathmatical Economics. 2. 67-85 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Kusuoka: "Laplace approximations for sums of independent random vectors"Prob. Theory. Rel. Fields. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Kusuoka: "Malliavin Calculus, Geometric Mixing, and Expansion of Diffusion Functionals"Prob. Theory. Rel. Fields. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Kusuoka: "Approximation of Expectation of diffusion processes and Mathmatical Finance"Proc. Taniguchi Conference 1998. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Kaise: "Deduction of some Bellman-Isaacs equations of ergodic type and their singular limits : relationships to eigenvalue problems of Schodinger operators"Proceedings of the 36th IEEE CDC Conference, san Diego. 3419-3423 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A. Bensousan: "Min-max characterization of a small noise limit on risk sensitive control"SIAM J. Control and Optimization. 35. 1093-1115 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A. Bensousan: "Some results on risk-sensitive with full observation"Appl. Math. and its Optimization. 37. 1-41 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Kaise: "Bellman-Issacs equations of ergodic type related to risk-sensitive control and their singular limit"Asymptotic Analysis. 16. 347-362 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Nagai: "Singular limit of Bellman-Issacs equations of ergodic type related to risk-sensitive control""Stochastic Analysis, Control, Optimization and Application, a volume in honor of W. H. Fleming" ed. W. M. McEneaney. 95-114 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Kaise: "Ergodic type Bellman equations of risk-sensitive control with large parameters and their singular limit"Asymptotic Analysis. 20. 279-299 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A. Bensousan: "Conditions for no breakdown and Bellman equations of risk sensitive control"Applied Mathmatics and Optimization. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Kaise: "Ergodic Type Bellman equation of risk-sensitive control"Proceedings of The 31st ISCIE International Symposium on Stochastic Systems Theory and Its Applications. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Sugita: "Holomorphic Wiener Function""New Trends in Stochastic Analysis", Proceedings of a Taniguchi International workshop at Charingworth Manor, World Scientific. 399-415 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Sugita: "Limit theorem for symmetric statics with respect to Weyl transformation: Dis-apperance of dependency"Jour. Math. Kyoto Univ.. 38. 653-671 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Sugita: "Oscillatory integrals with quadratic phase function on a real abstract Wiener space"J. Funct. Anal.. 155. 229-262 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Sugita: "A remark on stochastic oscillatory integrals with respect to a pinned measure"Kyushu Journal of Mathmatics. 53. 151-162 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Sugita: "Limit theorems for Weyl transformation in infinite-dimensional torus: Disappearance of dependency"Journal of the Faculty of Science, the University of Tokyo. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] I. Mitoma: "One loop approximation of the Chern-Simons integral"The Volume in Honor of 70th Birthday of T. Hida. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] I. Mitoma: "Wiener space approach to a perturbative Chern-Simons integral""Stochastic Processes, Physics and Geometry, New Interplays", Proceedings, Canad. Math. Soc.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Handa: "A lower bound for time correlations of lattice gases"Electron. Comm. probab.. 4. 1-8 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 長井英生: "確率微分方程式"共立出版. 227 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Li and Y.Ogura: "An optional sampling theorem for fuzzy valued martingales"Seventh International Fuzzy Systems Association World Congress. IV. 9-14 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A.Kasue, H.Kumura and Y.Ogura: "Convergence of heat kernels on a compact manifold"Kyushu J. Math.. 51. 453-524 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Li and Y.Ogura: "Convergence of set valued sub- and super-martingales in the kuratowski-Mosco sense"Ann. Prob.. 26. 1384-1402 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y.Ogura: "Stochastic fuzzy analysis"Jour. Japan Soc. Fuzzy Theory and Systems. 10. 2-9 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Li and Y.Ogura: "Convergence of set valued and fuzzy valued martingales and smartingales in the Kuratowski-Mosco sense"Proceedings Seventh International Conference IPMU. 72-79 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Li and Y.Ogura: "Convergence theorems for set valued and fuzzy valued martingales and smartingales"Jour. Korean Math. Soc.. 33. 765-782 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y.Ogura, M.Tomisaki and M.Tsuchiya: "Superposition of diffusion processes - Feller property""Trends in Probability and Related Analysis", eds. Kono, N.&N. R. Sieh, World Scientific Pub.. 113-128 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Li and Y.Ogura: "Convergence of set-valued and fuzzy-valued martingales"Fuzzy Sets and Systems. 101. 453-461 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Li and Y.Ogura: "An approximation theorem for unbounded fuzzy valued random variables"Proceedings of the Eighth International Fuzzy Systems Association World Congress. 2. 1042-1046 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Li and Y.Ogura: "Fuzzy Gaussian processes and martingale with continuous parameter"Proceedings of the Fifth Joint Conference on Information Sciences. 1. 146-149 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Li and Y.Ogura: "Convergence in graph for fuzzy valied martingales and smartingale""Statistical Modeling, Analysis and Management of Fuzzy Data" eds. M.A.Gil, Bertoluzza and D.A.Ralescu. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y.Ogura, S.Li and D.A.Ralescu: "Set defuzzification and Choquet integral"International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y.Ogura, M.Tomisaki and M.Tsuchiya: "Existence of strong solution for an integro-differential equation and superposition of diffusion processes"Stochastics in Finite/Infinite Dimensions (In honor of Gopinath Kallianpur). (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N.Ikeda and S.Kusuoka: "Short time asymptotics for fundamental solutions of heat equations with boundary conditions""New Trends in Stochastic Analysis", ed. K.D.Elworthy, S.Kusuoka and I.Schigekawa, World Scientific Pub.. 1. 182-219 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Kusuoka and X-Y.Zhou: "Waves on fractal-like manifolds and effective energy propagation"Prob. Theory Rel. Fields. 110. 473-495 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Kusuoka: "A remark on default risk models""Advances in Mathematical Economics" eds. S. Kusuoka, M. Maruyama. 1. 69-82 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Kusuoka: "Term Structure and SPDE""Advances in Mathematical Economics". 2. 67-85 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Kusuoka and S.Liang: "Laplace approximations for sums of independent random vectors"to appear in Prob. Theory Rel. Fields.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Kusuoka and N.Yoshida: "Malliavin Calculus, Geometric Mixing, and Expansion of Diffusion Functionals"to appear in Prob. Theory Rel. Fields.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Kusuoka: "Approximation of Expectation of diffusion processes and Mathematical Finance"Proc. Taniguchi Conference 1998. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Kaise and H.Nagai: "Deduction of some Bellman-Isaacs equations of ergodic type and their singular limits : relationships to eigenvalue problems of Schodinger operators""Proceedings of the 36-th IEEE CDC conference", San Diego. 3419-3423 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A.Bensousan and H.Nagai: "Min-max characterization of a small noise limit on risk sensitive control"SIAM J. Control and Optimization. 35. 1093-1115 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A.Bensousan, J.Freshe and H.Nagai: "Some results on risk-sensitive with full observation"Appl. Math. And its Optimization. 37. 1-41 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Kaise and H.Nakai: "Bellman-Isaacs equations of ergodic type related to risk-sensitive control and their singular limit"Asymptotic Analysis. 16. 347-362 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Nagai: "Singular limit of Bellman-Isaacs equations of ergodic type related to risk-sensitive control""Stochastic Analysis, Control, Optimization and Application, a volume in honor of W.H.Fleming", ed. W.M.McEneaney. 95-114 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Kaise and H.Nakai: "Ergodic type Bellman equations of risk-sensitive control with large parameters and their singular limit"Asymptotic Analysis. 20. 279-299 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A.Bensousan and H.Nagai: "Conditions for no breakdown and Bellman equations of risk sensitive control"Applied Mathematics and Optimization. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Kaise and H.Nagai: "Ergodic Type Bellman equations of risk-sensitive control"Proceedings of The 31st ISCIE International Symposium on Stochastic Systems Theory and Its Applications. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Sugita: "Holomorphic Wiener Function""New Trends in Stochastic Analysis", Proceeding of a Taniguchi International workshop at Charingworth Manor, World Scientific. 399-415 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Sugita and S.Takanobu: "Limit theorem for symmetric statistics with respect to Weyl transformation: Disappearance of dependency"Jour. Math. Kyoto Univ.. 38. 653-671 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Sugita and S.Taniguchi: "Oscillatory integrals with quadratic phase function on a real abstract Wiener space"J. Funct. Anal. 155. 229-262 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Sugita and S.Taniguchi: "A remark on stochastic oscillatory integrals with respect to a pinned measure"Kyushu Journal of mathematics. 53. 151-162 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Sugita and S.Takanobu: "Limit theorems for Weyl transformation in infinite-dimensional torus: Disappearance of dependency"Journal of the Faculty of Science, the Univeristy of Tokyo. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] I.Mitoma: "One loop approximation of the Chern-Simons integral""The Volume in Honor of 70th Birthday of T.Hida". (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] I.Mitoma: "Wiener space approach to a perturbative Chern-Simons integral""Stochastic Processes, Physics and Geometry, New Interplays", Proceedings, Canad. Math. Soc.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K.Handa: "A lower bound for time correlations of lattice gases"Electron. Comm. Probab.. 4. 1-8 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Nagai: "Stochastic Differential Equations"Kyoritsu Syuppan [Japanese]. 227 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y.Ogura: "Superposition of diffusion processes -Feller property-"in "Trends in Probability and Related Analysis ",eds.Kono,N.&N.R.Sieh. 113-128 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Li: "Convergence of set-valued and fuzzy-valued martingales"Fuzzy Sets and Systems. 101. 453-461 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Li: "An approximation theorem for unbounded fuzzy valued random variables"in "Proceedings of the Eighth International Fuzzy Systems Association World Congress". 2. 1042-1046 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Li: "Fuzzzy Gaussian processes and martingale with continuous parameter"in "Proceedings of the Fifth Joint Conference of Information Sciences". 1. 146-149 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Li: "Convergence in graph for fuzzy valued martingales and smartingale"in "Statistical Modeling,Analysis and Management of Fuzzy Data" eds.M.A.Gil,Bertoluzza and D.A.Ralescu. to appear.

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Ogura: "Fuzzy defuzzification and Choquet integral"International Jounal of Uncertainty,Fuzziness and Knowledge-Based Systems. to appear.

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Kusuoka: "Term Structure and SPDE"in "Advances in Mathematical Economics". 2. 67-85 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] I.Mitoma: "One loop approximation of the Chern-Simons integral"in "The Volume in Honor of 70th Birthday of T.Hida". (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] I.Mitoma: "Wiener space approach to a perturbative Chern-Simons integral"in "Stochastic Processes,Physics and Geometry,New Interplays",Proceedings,Canad.Math.Soc.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Handa: "A lower bound for time correlations of lattice gases"Electron.Comm.Probab.. 4. 1-8 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Kusuoka: "Laplace approximations for sums of independent random vectors"Prob.Theory Rel.Fields. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Kusuoka: "Malliavin Calculus,Geometric Mixing,and Expansion of Diffusion Functionals"Prob.Theory Rel.Fields. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Kusuoka: "Approximation of Expectation of diffusion processes and Mathematical Finance"in "Proc.Taniguchi Conference 1998". (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Kaise: "Ergodic type Bellman equations of risk-sensitive control with large parameters and their singular limit"Asymptotic Analysis. 20. 279-299 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] A.Bensousan: "Conditions for no breakdown and Bellman equations of risk sensitive control"Applied Mathematics and Optimization. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Sugita: "A remark on stochastic oscillatory integrals with respect to a pinned measure"Kyushu Journal of Mathematics. 53. 151-162 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Sugita: "Limit theorems for Weyl transformation in infinite-dimensional torus: Disappearance of dependency"Journal of the Faculty of Science,the University of Tokyo. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] 長井 英生: "確率微分方程式"共立出版. 227 (1999)

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      1999 Annual Research Report
  • [Publications] S.Li: "Convergence of set valued and fuzzy valued martingales" Fuzzy Sets and Systems. 100. 543-461 (1998)

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      1998 Annual Research Report
  • [Publications] S.Li: "Convergence of set valued sub-and super-martingales and smartingales in the Kuratowski-Mosco sense" Ann.Prob.26. 1384-1402 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Li: "Convergence of set valued and fuzzy valued martingales in the Kuratowski-Mosco sense" in"Proceedings Seventh International Conference IPMU". 72-29 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Kusuoka: "Waves on fractal-like manifolds and effective energy propagation" Prob.Ther.and Rel.Fields. 110. 473-495 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Kusuoka: "A remark on default risk models" in "Advances in Mathematical Economics" eds. S.Kusuoka,M.Maruyama. vol.1. 69-82 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Kaise: "Bellman-Isaacs equations of ergodic type related to risk-sensitive control and their singular limit" Asymptotic Analysis. 16. 347-362 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Nagai: "Singular limit of Bellman-Isaacs equations of ergodic type related to risk-sensitive control" in "Stochastic Analysis,Control,Optimization and Application,a volume in honor of W.H.Fleming"ed.W.M.McEneaney. 95-114 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] A.Bensousan: "Conditions for no breakdown and Bellman equations of risk sensitive control" Applied Mathematics and Optimization. to appear.

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Sugita: "Limit theorem for symmetric statistics with respect to Weyl transformation : Disap-pearance of dependency" Jour.Math.Kyoto Univ.38. (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Sugita: "Oscillatory integrals with quadratic phase function on a real abstract Wiener space" J.Funct.Anal.155. 229-262 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Sugita: "A remark on stochastic oscillatory integrals with respect to a pinned measure" kyushn Journal of Mathematics. to appear. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Li: "An optional sampling theorem for fuzzy valued martingales" IFSA'97 Prague Proceedings. IV. 9-14 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] A.Kasue: "Convergence of heat kernels on a compact manifold" Kyushu J.Math.51. 453-524 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Li: "Convergence of set valued and fuzzy valued martingales" Fuzzy Sets and Systems. 100(to appear). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Li: "Convergence of set valued sub- and super-martingales in the Kuratowski-Mosco sense" Ann.Prob.(to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Ikeda: "Short time asymptotics for fundamental solutions of heat equations with boundary conditions" in "New Trends in Stochastic Analysis",ed.K.D.Elworthy,S.Kusuoka and I.Schigekawa,World Scieneific Pub.182-219 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Kusuoka: "Waves on fractal-like manifolds and effective energy propagation" Prob.Ther.and Rel.Fields. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Kaise: "Deduction of some Bellman-Isaacs equations of ergodic type and their limit relation-ships to eigenvalue problems of Schodinger operators" Proceedings of the 36-th IEEE CDC Conference,San Diego. 3419-3423 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] A.Bensousan: "Min-max characterization of a small noise limit on risk sensitive control" SIAM J.Control and Optimization. 35. 1093-1115 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] A.Bensousan: "Some results on risk-sensitive with full observation" Appl.Math.and its Optimization. 37. 1-41 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Kaise: "Bellman-Isaacs equations of ergodic type related to risk-sensitive control and their singular limit" Asymptotic Analysis. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Sugita: "Holomorphic Wiener Function" in"New Trends in Stochastic Analysis",Proceeding of a Taniguchi International workshop at Charingworth Manor,World Scientific. 399-415 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Sugita: "Oscillatory integrals with quadratic phase function on a real abstract Wiener space" J.Funct.Anal.(to appear).

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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