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1998 Fiscal Year Final Research Report Summary

Research on random phenomena by the methods of modern mathematics

Research Project

Project/Area Number 07404005
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 InstitutionKYOTO UNIVERSITY

Principal Investigator

WATANABE Shinzo  Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90025297)

Co-Investigator(Kenkyū-buntansha) YOSHIDA Nobuo  Hokkaido Univ., Graduate School of Science, Lecturer, 大学院・理学研究科, 講師 (40240303)
KOKUBU Hiroshi  Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50202057)
SHIGEKAWA Ichiro  Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (00127234)
TANIGUCHI Masahiko  Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50108974)
NISHIDA Takaaki  Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70026110)
Project Period (FY) 1995 – 1998
KeywordsSobolev spaces on Wiener space / measure valued branching processes / Brownian snake / innovation problem / bifurcations for equations in fluid dynamics / bifurcation problem in dynamical system / complex dynamics of entirefunctions / lattice spin system
Research Abstract

We studied on problems of mathematical models in random phenomena ;
stochastic processes, functionals on Wiener path and loop spaces, lattice spin systems, dynamical systems and models in fluid dynamics. We list main results :
1. We defined Sobolev spaces on Wiener space and studied regularity of Wiener path integrals and conditional Wiener path integrals in terms of Sobolev spaces.
We obtained a comparison theorem for Markovian semigroups which can be applied to analysis on Wiener space.
2. We studied structures and operations concerning measure valued branching processes (superprocesses) by using the notion of Brownian snakes due to Le Gall.
We studied the innovation problem for stochastic processes and obtained some example of stochastic processes which generate non-cosy filtrations in the sense of Tsirelson.
3. We gave a computer aided proof in bifurcation problems for equations of fluid dynamics.
4. We studied on a degenerating singularity of vector fields inconnection with bifurcations and chaotic behavior of dynamical systems.
Also we obtained new results on bifurcations of homoclinic orbits.
5. We studied complex dynamical systems by the theory of Teichmuller spaces and constructed a theory of complex dynamics by entire functions.
6. We studied relaxation problem of Glauber dynamics in lattice spin systems.

  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] S.Watanabe: "Stochastic analyis on Wiener space" Proc.Norbert Wiener Centenary Congress, Appl.Math.Proc.Symp.52. 359-370 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Watanabe: "Branching diffusions (superdiffusions) and random snakes" Proc.SPA96, World Scientific. 416-429 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Watanabe: "The existence of a multiple spider martingale in the natural filtration of a certain diffusion in the plane" Seminaire de Probab.(Springer series of LNM). 33 発売予定. (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] I.Shigekawa: "L^p contraction semigroups for vector valued functions" J.Funct.Analysis. 147. 69-108 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Kokubo and V.Naudot: "Existence of infinitely many homoclinic doubling bifurcation from some codimension three homoclinic or bits" J.Differential Equations. 140. 309-364 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Yoshida: "Relaxed criteria of Dobrushin-Shlosman mixing condition" J.Stat.Physics. 87. 293-309 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 上田哲生・諸澤俊介・谷口雅彦: "複素力学系序説=フラクタルと複素解析=" 培風館, 東京, 240 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 重川一郎: "確率解析(岩波講座 現代数学の展開)" 岩波書店, 東京, 192 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Watanabe: "Stochastic analysis on Wiener space" Proc.Norbert Wiener Centenary Congress, Proc.Symmp.Appl.Math.AMS.52. 359-370 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Watanabe: "Branching diffusion (superdiffusions) and random snakes" Trends in Probability and Related Analysis, Proc.SPA'96, World Scientific. 289-304 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Watanabe: "The existence of a multiple spider martingale in the natural filtration of a certain diffusion in the plane" Seminaire de Probabilites XXXIII,Springer. to appear. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] I.Shigekawa: "L^p contraction semigroups for vector valued functions" J.Funct.Anal.147. 69-108 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Kokubu and Vincent Naudot: "Existence of infinitely many homoclinic doubling bifurcations from some codimension three homoclinic orbits" Journal of Dynamics and Differential Equations. 9. 445-462 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N.Yoshida: "Finite volume Glauber dynamics in a small magnetic field" J.Stat.Phys.90, Nos.3/4. 1015-1035 (1998)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1999-12-08  

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