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Study of infinite dimensional stochastic analysis and stochastic numerical analysis

Research Project

Project/Area Number 09440084
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 InstitutionKYUSHU UNIVERSITY

Principal Investigator

SUGITA Hiroshi  Kyushu Univ., Graduate School of Math, Asso.Prof., 大学院・数理学研究科, 助教授 (50192125)

Co-Investigator(Kenkyū-buntansha) OGAWA Shigeyoshi  Kanazawa Univ., Faculty of Engineering, Professor, 工学部, 教授 (80101137)
KUWAE Kazuhiro  Saga Univ., Faculty of Science and Engineering, Asso.Prof., 理工学部, 助教授 (80243814)
OGURA Yukio  Saga, Univ., Faculty of Science and Engneering, Professor, 理工学部, 教授 (00037847)
TANIGUCHI Setsuo  Kyushu Univ., Graduate School of Math., Asso.Prof., 大学院・数理学研究科, 助教授 (70155208)
KUNITA Hiroshi  Kyushu Univ., Graduate School of Math., Professor, 大学院・数理学研究科, 教授 (30022552)
佐藤 坦  九州大学, 大学院・数理学研究科, 教授 (30037254)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥7,600,000 (Direct Cost: ¥7,600,000)
Fiscal Year 1998: ¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 1997: ¥4,100,000 (Direct Cost: ¥4,100,000)
KeywordsWeyl transformation / numerical integration / Monte-Carlo method / Wiener space / multiple Wiener Integral / Oscillatory integral / Malliavin calculus / 移動積分 / Malliarin解析 / ウイナ-空間 / 停留位相法 / 多重ウイナ-積分 / 擬似乱数 / 確率微分方程式の数値解法 / 暗号理論
Research Abstract

Results in infinite dimensional stochastic analysis
SUGITA and TANIGUCHI investigated the oscillatory integrals on an abstract Wiener space and got the following result Let the phase function be a double Wiener integral and let the amplitude function be a multiple Wiener integral. If it is impossible to define properly the value of the amplitude function at the origin, the behavior of the oscillatory integral becomes quite different from finite dimensional cases.
SUGITA and TAKANOBU got the following result Let {f^<(m)>}_m be a sequence of symmetric statistics of m variables. Then the sequence of random variables {f^<(m)>(chi+nalpha)}_n on the *-dimensional torus converges as m * * to the i.i.d. of multile Wiener intgerals.
Results in stochastic numerical analysis
From Jan.27 to Jan.30, we held a reseach conference "Probability theorey and computational mathematics" at Kyushu University. SUGITA gave a talk there with title "Pseudorandom number generation by means of irrational rotation-Fourier series approach". From Nov.9 to Nov.11, we held a research conference "The theory and methods of stochastic numerical analysis" at Kanazawa university. SUGITA gave a talk there with title "Robustness of quasi-Monte Carlo methods".

Report

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

    (24 results)

All Other

All Publications (24 results)

  • [Publications] H.Sugita: "Holomorphic Wiener function" New trends in stochastic analysis, World Sci. Publ.399-415 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Sugita: "Pseudorandom numbers from the viewpoint of Computational complexity theory(Japanese)" Problems in stochastic numerical analysis, 京大数理研講究録. 1032. 118-124 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Sugita: "A pseodorandom number generation method that utilizes inational rotations -a numerical analysis approach using probability theory(Japanese)" Pseudorandom numbers and chaos, 京大数理研講究録. 1011. 77-88 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Sugita and S.Takanobu: "Limit theorem for symmetric statistics with respect to Weyl transformation : Disappearance of dependency" J.Math.Kyoto Univ.,. 38-4印刷中. (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Sugita and S.Taniguchi: "A remark on stochastic oscillatory integrals with respect to a pinned measure" Kyushu J.of Math.印刷中. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 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・1. 229-262 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Sugita: "Holomorphic Wiener function." New trends in stochastic analysis (Charingworth, 1994), 399-415, World Sci.Publishing, River Edge, NJ. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Sugita: "Pseudorandom numbers from the viewpoint of Computational complexity theory. (Japanese)" Problems in stochastic numerical analysis, III (Japanese) (Kyoto, 1997). Surikaisekikenkyusho Kokyuroku. No.1032. 118-124 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Sugita: "A pseudorandom number generation method that utilizes irrational rotations-a numerical analysis approach using probability theory. (Japanese)" Pseudorandom numbers and chaos (Japanese) (Kyoto, 1996.). Surikaisekikenkyusho Kokyuroku. No.1011. 77-88 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Sugita and S.Takanobu: "LimitTheorem for symmetric statistics with respect to Weyl transformation : Disappearance of dependency" J.Math.Kyoto Univ.38-4. (1998)

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

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 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.155-1. 229-262 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Sugita and S.Takanobu: "Limit theorem for symmetric statistics with respect to Weyl tronsformation: Disappearana of dependency" J.Math.Kyoto Univ.38・4(印刷中). (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Sugita and S.Taniguchi: "A remark on stochastic oscillatory integrals with respoat to apinmed measure" Kyushu J. of Math.(発売予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Sugita and S.Taniguchi: "Oscillatory integrals with gnadratic phase furction on a real abstrect Wiener space" J.Farct.Anal.155-1. 229-262 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Ogara and L.Shoumei: "Convergence of set valued sad-and sapermartingale in the Kuratowski-Mosco sense" Ann.Probab.26・3. 1384-1402 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Taniguchi: "On the eyponential decay of oscillatory integrals on an abstract Wianer space" J.Farct.Anal.154・2. 424-443 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Kuwae: "Functional calculus for Dirichhet forms" Osaka J.Math.35・3. 683-715 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiroshi Sugita: "Holomorphic Wiener Function" New Trends in Stochastic Analysis(Rrocedings of Taniguchi Symp.). 399-415 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Sugita: "Ocillatory integrals with quadratic phase function on a real abstract Wiener space" Journ.of Function Analysis(発表予定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Taniguchi: "Analytic functions,Cauchy formula,and stationary phase on a real abstract Wiener space" Journ.of Function Analysis. 143-2. 420-528 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hiroshi Kunita: "Infinitesimal generators of nonhomogeneous convolution semigroups on Lie groups" Osaka Journ.of Mathematics. 34-1. 233-264 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Y.Ogura: "Convergeuce of irest kernels on a compact manifold" Kyushu Journ.of Mathematics. 51-2. 453-524 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Kuwae: "Weak convgergence of syminetric diffudion pcocesses" Probab.Theory Relatecl Fields. 109-2. 159-182 (1997)

    • Related Report
      1997 Annual Research Report

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

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