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Synthetic Research of Probability Theory

Research Project

Project/Area Number 11304003
Research Category

Grant-in-Aid for Scientific Research (A)

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

Principal Investigator

FUNAKI Tadahisa  School of Mathematical Sciences, The University of Tokyo, Professor, 大学院・数理科学研究科, 教授 (60112174)

Co-Investigator(Kenkyū-buntansha) SHIGEKAWA Ichiro  University, Graduate School of Science, Professor, 理学研究科, 教授 (00127234)
UCHIYAMA Kohei  Tokyo Institute of Technology, Graduate School of Science and Engineering, Professor, 理工学研究科, 教授 (00117566)
TAKEDA Masayoshi  Tohoku University, Graduate School of Science, Professor, 理学研究科, 教授 (30179650)
HIGUCHI Yasunari  Faculty of Science, Kobe University, Professor, 理学部, 教授 (60112075)
NAGAI Hideo  Graduate School of Engineering Science, Osaka University, Professor, 基礎工学研究科, 教授 (70110848)
Project Period (FY) 1999 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥29,200,000 (Direct Cost: ¥26,200,000、Indirect Cost: ¥3,000,000)
Fiscal Year 2001: ¥13,000,000 (Direct Cost: ¥10,000,000、Indirect Cost: ¥3,000,000)
Fiscal Year 2000: ¥9,400,000 (Direct Cost: ¥9,400,000)
Fiscal Year 1999: ¥6,800,000 (Direct Cost: ¥6,800,000)
KeywordsStochastic analysis / Markov processes / Hydrodynamic limit / Random matrices / Stochastic control / Ergodic theory / Infinite particles' system / Dirichlet form
Research Abstract

This research was accomplished by 25 members under strong helps from many researchers in probability theory and related fields. During three years of the research period, 27 meetings were organized and 21 researchers were invited from abroad. A lot of research products were obtained in broad area:
1. Related to the basic theory in probability theory, extension of the inverse arcsine law to one dimensional diffusion processes, properties of Brownian motion/heat kernel/Green function on several spaces, Markov processes and Dirichlet form, infinite dimensional stochastic analysis, stationary phase method and asymptotic theory and others were discussed.
2. As applications of probability theory, mathematical physics such as analysis of phase separating surface arising under phase transitions, derivation of free boundary problem, motion of interacting Brownian hard balls, scaling limit of percolation cluster, random matrix, stochastic processes on fractals, problem of risk sensitive stochastic control, ergodid theory especially law of large numbers for ψ-mixing random variables, numerical calculation for stochastic differential equations and nonlinear diffusion equations, asymptotic expansion and applications of Malliavin calculus in mathematical statistics, problems related to differential geometry like collapse of manifolds.
Concrete explanations on each research result can be found in the booklet of the research report in details. As is stated above, under the project of this research, many foreign researchers were invited and it was very fruitful and extremely important for the development of the probability theory in Japan in future.

Report

(4 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • Research Products

    (100 results)

All Other

All Publications (100 results)

  • [Publications] T.Funaki: "Fluctuations for ▽φ interface model on a wall"Stoch. Proc. Appl.. 94. 1-27 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Bensoussan, H.Nagai: "Conditions for no breakdown and Bellman equatuins of Risk-sensitive control"Appl. Math. Optim.. 42. 91-101 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Osada: "A family of diffusion processes on Sierpinski carpets"Probab. Theory Related Fields. 119. 275-310 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y.Higuchi: "On the speed of convergence for two-dimensional first passage Ising percolation"Ann. Probab.. 28. 353-378 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] S.Taniguchi: "Analytic functions on abstract Winere spaces"J. Funct. Anal.. 179. 235-250 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Matsumoto: "A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration"Osaka J. Math.. 38. 383-398 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 舟木直久: "ミクロからマクロへ 1.界面モデルの数理"シュプリンガー・フェアラーク東京(予定). 300 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Funaki: "Fluctuations for ▽φ interface model on a wall"Stoch. Proc. Appl.. 94. 1-27 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Bensoussan (H. Nagai): "Conditions for no breakdown and Bellman equations of Risk-sensitive control"Appl. Math. Optim.. 42. 91-101 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Osada: "A family of diffusion processes on Sierpinski carpets"Probab. Theory Related Fields. 119. 275-310 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y. Higuchi: "On the speed of convergence for two-dimensional first passage Ising percolation"Ann. Probab.. 28. 353-378 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] S. Taniguchi: "Analytic functions on abstract Wiener spaces"J. Funct. Anal.. 179. 235-250 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Matsumoto: "A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration"Osaka J. Math.. 38. 383-398 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Funaki: "From Micro to Macro 1. Mathematical Approach to Interface Models"Springer-Verlag Tokyo (in press) (In Japanese). 300 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Funaki: "Fluctuations for $\nabla \phi$ interface model on a wall"Stoch. Proc. Appl.. 94. 1-27 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] C.^-Kraaikamp (H.^-Nakada): "On a Problem of Schweiger Concerning Normal Numbers"Journal of Number Theory. 86. 330-340 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y. Ogura: "Weak convergence of laws of stochastic processes on Riemannian manifolds"Prob. Theor. Rel. Fields. 119. 529-557 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.^-Osada: "A family of diffusion processes on Sierpinski carpets"Probab. Theory Related Fields. 119. 275-310 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] S.^-Taniguchi: "Analytic functions on abstract Winere spaces"J. Funct. Anal.. 179. 235-250 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.^-Matsumoto: "A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration"Osaka J. Math.. 38. 383-398 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 舟木直久: "ミクロからマクロへ, 1. 界面モデルの数理"シュプリンガー・フェアラーク東京(予定). 300 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Funaki: "Recent results on the Ginzburg-Landau $\nabla \bhi$ interface model."Hydrodynamic Limits and Related Topics,. 71-81 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Funaki: "Large deviations for the Ginzburg-Landau $\nabla \phi$ interface model."to appear in Probab.Theory Relat.Fields,. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Funaki: "Fluctuations for $\nabla \phi$ interface model on a wall."to appear in Stoch.Proc.Appl.,. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Mikami: "Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric."Appl.Math.Optim.. 42. 203-227 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Takeda: "$L^p$-independence of the spectral radius of symmetric Markov semigroups."Stochastic Processes, Physics and Geometry : New Interplays.. (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Uchiyama: "Uniqueness of solutions to the initial value problem for anintegro-differential equation."Diff.Int.Eoqs.. 13. 401-422 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Fradon(H.Tanemura): "An infinite system of Brownian balls with infinite range interaction."Stoch.Proc.Appl.. 90. 43-66 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Osada: "Tagged particles of interacting Brownian motions with skew symmetric drifts."to appear in Monte Carlo Methods and Applications.. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Hariya(H.Osada): "Diffusion processes on path spaces with interactions."to appear in Rev.\ Math.\ Phys.. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Osada: "A family of diffusion processes on Sierpinski carpets."to appear in Probab.Theory Related Fields.. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Matsumoto: "Quadratic Hamiltonians, Wiener functionals and the metaplectic representations."J.Math.Soc.Japan.,. 52. 269-292 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Matsumoto: "An analogue of Pitman's $2M-X$ theorem for exponential Wiener functionals, Part I : A time-inversion approach."Nagoya Math.J.. 159. 125-166 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Uchiyama: "A non-linear evolution equation driven by a logarithmic potential."Bull.London Math.Soc.. 32. 353-363 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] J.Aaronson(H.Nakada): "Multiple Recurrence of Markov Shifts and Other Infinite Measure Preserving Transformations."Israel Journal of Mathematics,. 117. 285-310 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] C.Kraaikamp(H.Nakada): "On Normal Numbers for Continued Fractions."Ergodic Theory and Dynamical Systems,. 20. 1405-1421 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] V.Berthe(H.Nakada): "On Continued Fraction Expansions in Positive Characteristic : Equivalence Relations and Some Metric Propertie"Expositiones Mathematicae,. 18. 257-284 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Kasahara: "Large deviation around origin for sums of nonnegative i.i.d.random variables."Nat.Sci.Rep.Ocha.Univ.,. 51. 27-31 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Katori(H.Tanemura): "Survival probability for discrete time models in one dimension."J.Statist.Phys.. 99. 603-612 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Ogura(+富崎松代): "Existence of a strong solution for an integro-differential equation and superposition of diffusion processes."Stochastics in Finite and Infinite Dimensions. 341-359 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Hara: "The scaling limit of the incipient infinite cluster in high-dimensional percolation.I.Critical exponents."J.Statist.Phys.. 99. 1075-1168 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Hara: "The scaling limit of the incipient infinite cluster in high-dimensional percolation.II.Integrated super-Brownian excursion."J.Math.Phys.. 41. 1244-1293 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Kuroda(H.Nagai): "Ergodic type Bellman equation of risk sensitive control and portfolio optimization on infinite time horizon."Optimal Control and Partial Differential Equations,. 530-538 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] 長井英生: "リスク鋭感的確率制御と数理ファイナンス"システム/制御/情報. 44. 447-454 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Taniguchi: "L\'evy's stochastic area and the principle of stationary phase."J.Funct.Anal.. 172. 165-176 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Ushima: "Certain ratio limit theorem for time inhomogeneous Markov chains."Stochastic Processes, Phisics and Geometry, New Interplays. 28. (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] I.Mitoma: "Infinite level asymptotics of a perturbative Chern-Simons integra Stochastics in Finite and Infinite Dimensions."Birkh\"auser,. 303-319 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Ogura(+富崎松代): "Superposition of diffusion processes-Feller Property-."Trends in Probability and related analysis.. 113-128 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] R.Bass and T.Kumagai: "Laws of the iterated logarithm for some symmetric diffusion processes."Osaka J.Math.,. 37. 625-650 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Kumagai: "Stochastic processes on fractals and related topics, Sugaku Expositions."Amer.Math.Soc.,. 13. 55-71 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Kaise(H.Nagai): "Ergodic type Bellman equation of risk-sensitive control."Proceedings ofthe 31st ISCIE International Symposium. 89-94 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] A.Bensoussan(H.Nagai): "Conditions for no breakdown and bellman equatuins of Risk-sensitive control."Appl.Math.Optim. 42. 91-101 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Nagai: "Risk-sensitive dynamic asset management with partial information."Stochastics in finite and infinite dimensions,. 321-340 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Nagai: "Risk-sensitive portfolio optimization with partial information."Proceedings of the 39-th CDC conference,. 1206-1211 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] C.Donati-Martin(H.Matsumoto): "On positive and negative moments of the integral of geometric Brownian motions."Stat.Prob.Lett.,. 49. 45-52 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] I.Shigekawa: "The domain of a generator and the intertwining property."Stochastics in Finite and Infinite Dimensions,. 401-410 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] N.Yoshida: "Application of log-Sobolev inequalitv to the stochastic dynamics of unbounded spin systems on the lattice."J. Funct.Anal.. 173. 74-102 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Kumagai: "Brownian motion penetrating fractals-An application of the trace theoremof Besov spaces."J.Func.Anal.,. 170. 69-92 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] G.Ben Arous and T.Kumagai: "Large deviations for Brownian motion on the Sierpinski gasket."Stoch.Proc. Their Appl.,. 85. 225-235 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] B.M.Hambly,T.Kumagai,S.Kusuoka and X.Y.Zhou: "Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets."J.Math.Soc.Japan,. 52. 373-408 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 舟木直久: "確率微分方程式(第2版)"岩波書店. 203 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T. Funaki: "Free boundary problem from stochastic lattice gas model"Ann. Inst. Henri Poincar\' e. 35. 573-603 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] T. Funaki: "Singular limit for stochastic reaction-diffusion equation and generation of random interfaces"Acta Mathematica Sinica, English Series. 15. 407-438 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] T. Funaki: "Recent results on the Ginzburg-Landau $\nabla \phi$ interface model.to appear in Proceedings of the Workshop on "Hydrodynamic Limits""Fields Institute Communications and Monograph Series. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] P. Biler (T. Funaki): "Interacting jump Markov processes associated with nonlocal quadratic evolution problems"Probability and Mathematical Statistics. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Mikami: "Markov marginal problems and their applications to Markov optimal control"Stochastic Analysis, Control, Optimization and Applications. 457-476 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Takeda Masayoshi: "Exponential decay of lifetime and a Theorem of Kac on total occupation times"Potential Anal.. 11. 235-247 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Takeda Masayoshi: "Topics on Dirichlet forms and symmetric Markov processes"Sugaku Expositions. 12. 201-222 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Fukushima, Masatoshi (M. Takeda): "Large deviations and LIL's for Brownian motlons on nested fractals"Osaka J.Math.. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Takeda Masayoshi: "$L p$-independence of the spectral radius of symmetric Markov processes"Proceedings of "International Conference on Infinite Dimensional (Stochastic) Analysis and Quantum Physics". (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 南 就将: "Level statistics for quantum Hamiltonians--Some preliminary ideas toward mathematical justification of the theory of Berry and Tabor"Proceedings of the Second Congress ISAAC. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] N. Minami: "On the Poisson limit theorems of Sinai and Major"Communications in Mathematical Physics. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] K. Uchiyama: "Uniqueness of solutions to the initial value problem for an integro-differential equation"Diff. Int. Eqs.. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] K. Uchiyama: "A non-linear evolution equation driven by a logarithmic potential"Bull. London Math. Soc.. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y. Kasahara: "On tail probability of local times of Gaussian processes"Stoch. Proc. Appl.. 82. 15-21 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y. Kasahara: "A note on the Local Time of Fractional Brownian Motion"J. Theoret. Probab.. 12. 207-216 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y. Kasahara: "Tail probability of local times of Gaussian processes and diffusions"Probability and Related Analysi eds. N. Kono & N. R. Shieh, World Scientific. 239-248 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 仲田 均: "Multple Recurrence of Markov Shifts and Other Infinite Measure Preserving Transformations"Israel Journal of Mathematics. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 種村秀紀: "Survival probability for discrete time model in one dimension"Journal of Statistical Physics. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] N. Ikeda (H. Matsumoto): "Brownian motion on the Hyperbolic plane and Selberg trace formula"J. Func. Anal.. 163. 63-110 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Matsumoto: "A version of Pitman' s $2M-X$ theorem for geometric Brownian motions"C. R. Acad. Sci. Paris. 328. 1067-1074 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Matsumoto: "Some change of probabilities related to a geometric brownian motion version of Pitman' s $2M-X$ theorem"Elect. Comm. Prob.. 4. 15-23 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Matsumoto: "Quadratic Hamiltonians, Wiener functionals and the metaplectic representations"J. Math. Soc. Japan. 52. 269-292 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Matsumoto: "An analogue of Pitman' s $2M-X$ theorem for exponential Wiener functionals, Part I : A time-inversion approach"Nagoya Math. J.. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Matsumoto: "An analogue of Pitman' s $2M-X$ theorem for exponential Wiener functionals, Part II : the role of generalized inverse Gaussian distributions"Nagoya Math. J.. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] C. Donati-Martin (H. Matsumoto): "On positive and negative moments of the integral of geometric Brownian motions"Stat. Prob. Lett.. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] I.. Shigekawa: "Semigroup domination on a Riemannian manifold with boundary"special volume of Takeyuki Hida. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Nagai: "Singular Limits of bellman Equations of Ergodic Type Related to Risk-Sensitive Control"Stochastic Analysis, Control, Optimization and Applications, a volume in honor of W. H. Fleming. 95-114 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] A. Bensoussan (H. Nagai): "Conditions for no breakdown and Bellman equations of risk sensitive control"Applied Math. Optim.. (2000)

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

    • Related Report
      1999 Annual Research Report
  • [Publications] Y. Ogura (M. Tomisaki): "Superposition of diffusion processes -- Feller Property --"Treds in Probability and related analysis. 113-128 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. O. Georgii (Y. Higuchi): "Percolation and number of phases in the 2D lsing model"J. Math. Phys.. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y. Higuchi: "On the speed of convergence for two dimensional first-passage lsing percolation"Annals of Probability. (2000)

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

    • Related Report
      1999 Annual Research Report
  • [Publications] S. Taniguchi: "Stochastic oscillatory integrals with quadratic phase function and Jacobi equation"Probability Theory and Related Fields. 114. 291-308 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] S. Taniguchi: "L\' evy' s stochastic area and the principle of stationary Phase"Journal of Functional Analysis. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] I. Mitoma: "One loop approximation of the Chern-Simons integral"the volume in honor of 70th birthday of T. Hida. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] I. Mitoma: "Wiener space approach to a perturbative Chern-Simons integral"Stochastic-Processes, Physics and Geometry, New Interplays Proceedings, Canad. Math. Soc.. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y. Oshima: "Certain ratio limit theorem for time inhomogeneous Markov chains"Stochastic Processes, Physics and Geometry : New Interplays A volume in Honor of Sergio Albeverio. (2000)

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

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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