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Integrated Research on The Up-to-Date Problems in Stochastic Numerics

Research Project

Project/Area Number 15340028
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 InstitutionRitsumeikan Univ.

Principal Investigator

OGAW Shigeyoshi  Ritsumeikan Univ., Dept. of Mathematics, Professor, 理工学部, 教授 (80101137)

Co-Investigator(Kenkyū-buntansha) MORI Makoto  Nihon Univ., Dept. of Humanities and Sci., Professor, 文理学部, 教授 (60092532)
ITO Shunji  Kanazawa univ., Graduate School of Sciences, Professor, 自然科学研究科, 教授 (30055321)
NINOMIYA Shoiti  Tokyo Inst.of Tech., Graduate School of Management, Professor, マネジメント研究科, 教授 (70313377)
FUKUYAMA Katsushi  Kobe Univ., Dept. of Mathematics, Professor, 理学部, 教授 (60218956)
SUGITA Hiroshi  Osaka Univ., Graduate School of Sciences, Professor, 理学研究科, 教授 (50192125)
Project Period (FY) 2003 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥14,400,000 (Direct Cost: ¥14,400,000)
Fiscal Year 2006: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2005: ¥4,700,000 (Direct Cost: ¥4,700,000)
Fiscal Year 2004: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2003: ¥5,300,000 (Direct Cost: ¥5,300,000)
KeywordsNumerical Solution of the SDE / Stochastic Numerics / Noncausal Stochastic Calculus / Stochastic Solution of Functional Equations / Numerical Integration / Random Numbers / Mathematical Finance / 確率微分方程式の数値解法 / 確立微分方程式の数値解法 / 非因果的確率解法
Research Abstract

The principal aim of this project was to develop the integrated researches on the comteporain problems in stochastic numericas as follows (names in paratheses ( ) are main investigators occupying each session);
(1) Numerical integration by means of Monte Carlo Methods and random numbers (S.Ito, M.Mori, K.Fukuyama, H.Sugita, and S.Ogawa)
(2) Numerical solution of the SDEs (S.Ninomiya and S.Ogawa)
(3) Noncausal calculus based on the Ogawa integral and its applications (S.Ogawa)
(4) Probabilistic solution of functional equations (K.Nishioka, S.Ogawa)
(5) Development of stochastic methods and algorithms for problems in OR, Finance, Computer sciences and Mathematical economy. (S.Ninomiya, K.Nishioka and S.Ogawa)
Through the whole period of the research activity, from 2003 to 2006, each research group cited above has pursuived each research plan, in a pararel way or sometimes in collaboration with other groups and as an integrated research group got many fruitful results not only theoretical but also the results of pratical importance, like the establishment of some computational algorithms in mathematical finance.

Report

(5 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (49 results)

All 2007 2006 2005 2004 2003 Other

All Journal Article (38 results) Book (4 results) Publications (7 results)

  • [Journal Article] Pricing rule in asymetric informations2007

    • Author(s)
      S.Ogawa, M.Pontier
    • Journal Title

      ESAIM : Probability and Statistics 11

      Pages: 80-88

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Noncausal Calculus Revisitted - around the so-called Ogawa integral2007

    • Author(s)
      S.Ogawa
    • Journal Title

      the Proc. of Math Conference in Quy-Nhon (to appear in)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Two dimensional linear dynamical systems with small random terms2007

    • Author(s)
      K.Nishioka
    • Journal Title

      Stocahstic Economic Dynamics, (ed. by B.S.Jensen, CBS) (to appear in)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Real Time Scheme for the Estimation of Volatilities2007

    • Author(s)
      S.Ogawa, K.Wakayam
    • Journal Title

      Proceedings of Faculty of Sciences and Technology, Ritsumeikan University

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Pricing Rule in Asymmetric Informations2007

    • Author(s)
      S.Ogawa, M.Pontier
    • Journal Title

      Les Actes du Colloque pour Celebration de son 60-eme anniversaire de Prof N.El-Karoui".

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stochastic Processes and Applications to Mathematical Finance2007

    • Author(s)
      S.Ogawa, J.Akahori, S.Watanabe
    • Journal Title

      Proceedings of the 6th Ritsumeikan International Symposium (World Scientific Publishing Co.) (Monograph)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Pricing rule in asymetric informations2007

    • Author(s)
      S.Ogawa, M.Pontier
    • Journal Title

      ESAIM : Probability and Statistucs 11

      Pages: 80-88

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Noncausal Calculus Revisitted--around the so-called Ogawa Integral2007

    • Author(s)
      S.Ogawa
    • Journal Title

      (the Proc. of Math Conference in Quy-Nhon (to appear in)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Two dimensional linear dynamical systems with small random terms2007

    • Author(s)
      K.Nishioka
    • Journal Title

      Stocahstic Economic Dynamics,ed. by B.S.Jensen,CBS (to appear in)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Noncausal stochastic integral equations of Fredholm type2006

    • Author(s)
      S.Ogawa
    • Journal Title

      "Harmonic, Wavelet and p-Adic Analysis" World Scientific

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Atomic surfaces, tilings and coincidences I. Irreducible case2006

    • Author(s)
      Shunji Ito, Hui Rao
    • Journal Title

      Israel J. Math 153

      Pages: 129-155

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Gap series and functions of bounded variation2006

    • Author(s)
      K.Fukuyama
    • Journal Title

      Acta Mathematica Hungarica 110

      Pages: 175-191

    • NAID

      120005980769

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Noncausal Integral Equations of Fredholm Type2006

    • Author(s)
      S.Ogawa
    • Journal Title

      the "Harmonic, Wavelet and p-Adic Analysis" World Scientific (to appear in)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stochastic Processes and Applications to Mathematical Finance2006

    • Author(s)
      S.Ogawa, J.Akahori, S.Watanabe
    • Journal Title

      Proceedings of the 5th Ritsumeikan International Symposium (World Scientific Publishing Co.) (Monograph)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] The 7th Workshop on Stochastic Numerics2006

    • Author(s)
      S.Ogawa (edt)
    • Journal Title

      Proceedings of RIMS Workshop (Monograph) (RIMS Publications)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Noncausal stochastic integral equations of Fredholm type2006

    • Author(s)
      S.Ogawa
    • Journal Title

      in "Harmonic,Wavelet and p-Adic Analysis" World Scienthific

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Atomic surfaces, tilings and coincidences I. irreducible case2006

    • Author(s)
      Shunji Ito, Hui Rao
    • Journal Title

      Israel J.Math 153

      Pages: 129-155

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Gap series and functions of bounded variation2006

    • Author(s)
      K.Fukuyama
    • Journal Title

      Acts Mathematica Hungarica 110

      Pages: 175-191

    • NAID

      120005980769

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Pricing rule in asymetric informations2006

    • Author(s)
      S.Ogawa, M.Pontier
    • Journal Title

      SMAIE saim PS (to appear in)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Noncausal Calculus Revisitted--around the so-called Ogawa integral2006

    • Author(s)
      S.Ogawa
    • Journal Title

      the Proc.of Math Conference in Quy-Nhon (to appear in)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Noncausal stochastic integral equations of Fredholm type2006

    • Author(s)
      S.Ogawa
    • Journal Title

      the Proc.of Math Conference in Quy-Nhon (to appear in)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Noncausal Stochastic Calculus revisited---around the so-called Ogawa integral2005

    • Author(s)
      S.Ogawa
    • Journal Title

      The Proc.of the Conference on Pure and Applied Math., held at Quy Nhon Univ. of Vietnam (to appear in)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Introduction to the numerical solution of the SDE2005

    • Author(s)
      S.Ogawa
    • Journal Title

      SUGAKU EXPOSITIONS, American Mathematical Society vol.18, No.1

      Pages: 101-122

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] The numerical solution of the SDE-Prat 2,2005

    • Author(s)
      S.Ogawa, S.Kanagawa
    • Journal Title

      SUGAKU EXPOSITIONS, American Mathematical Society vol.18, No.1

      Pages: 25-39

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Introduction to the discrete approximation of SDEs2005

    • Author(s)
      S.Ogawa
    • Journal Title

      SUGAKU Expositions, Amer.Math.Soc. 18-1

      Pages: 101-122

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On a BPE model for the Burgers' equations2004

    • Author(s)
      S.Ogawa, A.Kohatsu-Higa
    • Journal Title

      Publications of RIMS, RIMS of Kyoto University vol. 40, no.2

      Pages: 487-505

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Non linear feedback effects by hedging strategies2004

    • Author(s)
      S.Ogawa, M.Mancino
    • Journal Title

      Proc.of the Intern. Colloquium on Mathematical Finances and Stochastic Processes, held in March 2003 at Ritsumeikan Univ. (Inter Science Publ. Boston)

      Pages: 255-270

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Noncausal Cauchy problem for the noncausal SDEs2004

    • Author(s)
      S.Ogawa
    • Journal Title

      Proc.of the Intern. Colloquium on Mathematical Finances and Stochastic Processes, held in March 2003 at Ritsumeikan Univ. (Inter Science Publ. Boston)

      Pages: 289-304

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] The 6th Workshop on Stochastic Numerics2004

    • Author(s)
      S.Ogawa (edt)
    • Journal Title

      Proceedings of RIMS Workshop (Monograph) (RIMS Publications)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Noncausal Cauchy problem for the noncasual SDEs2004

    • Author(s)
      S.Ogawa
    • Journal Title

      Proceedings of the Intern.Colloq.Math.Finances and Stochastic Processes, World Scientific, Boston (2004)

      Pages: 289-304

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Non linear feedback effects by hedging strategies2004

    • Author(s)
      S.Ogawa, M.E.Mancino
    • Journal Title

      Proceedings of the Intern.Colloq.Math.Finances and Stochastic Processes, World Scientific, Boston (2004)

      Pages: 255-270

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On a BPE model for the Burgers equation2004

    • Author(s)
      S.Ogawa, A.Kohats-Higa
    • Journal Title

      Publications of RIMS, Kyoto University (2004) 40-2

      Pages: 487-505

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A quasi-random walk methods for one-dim. reaction-diffusion equations,2003

    • Author(s)
      S.Ogawa, C.Lecot
    • Journal Title

      Math. and Computers in Simulation (Elsevier Science B.V.) vol. 62

      Pages: 487-494

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On a discrete stochastic approximation and its applications to data analysis,2003

    • Author(s)
      S.Ogawa, S.Ogihara
    • Journal Title

      Monte Carlo Methods and Applications (VSP Publisher, Utrecht, Boston) vol.9, Np.1

      Pages: 39-50

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Report on the numerical experiments of Haselgrove's method applied to the numerical solution of the PDE2003

    • Author(s)
      S.Ogawa, T.Takemi
    • Journal Title

      Math. and Computers in Simulation (Elsevier Science B.V.) vol. 62, No.3-6

      Pages: 539-552

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A quasi-random walk method for one-dimensional reaction-diffusion equations2003

    • Author(s)
      S.Ogawa, C.Lecot
    • Journal Title

      Math.and Computers in Simulation, Elsevier Science B.V. 6-2

      Pages: 487-494

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On a discrete stochastic approximation and its applications to data analysis2003

    • Author(s)
      S.Ogawa, S.Ogihara
    • Journal Title

      Monte Carlo Methods and Applications, VSP Publisher, Netherland 9-1

      Pages: 39-50

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A numerical study of the Smile effect in implied volatilities induced by nonlinear feedbacks from hedging strategies.2003

    • Author(s)
      S.Ogawa, M.Mancino, S.Sanfelici
    • Journal Title

      Math.and Computers in Simulation, Elsevier Science B.V. 62,3-6

      Pages: 539-552

    • Related Report
      2004 Annual Research Report
  • [Book] Stochastic Processes and Applications to Mathematical Finance2006

    • Author(s)
      S.Ogawa, J.Akahori, S.Watanabe
    • Total Pages
      400
    • Publisher
      World Scientific, London, Singapore etc.
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2005 Annual Research Report 2004 Annual Research Report
  • [Book] Stochastic Processes and Applications to Mathematical Finance2006

    • Author(s)
      S.Ogawa, J.Akahori, S.Watanabe
    • Total Pages
      400
    • Publisher
      Woeld Scientific, London.Singapore etc.
    • Related Report
      2006 Annual Research Report
  • [Book] 確率解析と伊藤過程2005

    • Author(s)
      小川重義
    • Total Pages
      182
    • Publisher
      朝倉書店
    • Related Report
      2005 Annual Research Report
  • [Book] 微積分入門2004

    • Author(s)
      小川重義, 森真
    • Total Pages
      262
    • Publisher
      培風館
    • Related Report
      2004 Annual Research Report
  • [Publications] OGAWA, S.: "Noncausal Cauchy problem for the noncausal SDEs"Proceeding of the Intern.Conference on Stochastic Processes and Applications to Mathematical Finance. (to appear). 350 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] OGAWA, S., KOHATSUHIGA, A: "On a BPE model for the Burgers equation"RIMS Publications, RIMS Kyoto-Univ.. (to appear). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] MANCINO, M, OGAWA, S.: "Non linear feedback effects by hedging strategies"Proceeding of the Intern.Conference on Stochastic Processes and Applications to Mathematical Finance. (to appear). 350 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] OGAWA, S., LECOT, C.: "A quasi-random walk method for one-dimensional reaction diffusion equation"Math.Computu.Simulation Elsevier Science B.V.. 62・3-6. 487-494 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] OGAWA S, OGIHARA S: "On a discrete stochastic approximation and its application to data analysis"Monte Carlo Methods and Appl.VSP Netherland. 9・1. 39-50 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] SUGITA, H., TAKANOBU, S.: "The probability of two integers to be co-prime, revisited"OSAKA J.Math. 40・4. 945-976 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 小川重義, 森真: "微分積分学入門"培風館. 250 (2004)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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