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1996 Fiscal Year Final Research Report Summary

Probabilistic and Analytical Research of White Noise System

Research Project

Project/Area Number 07454033
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 InstitutionHIROSHIMA UNIVERSITY

Principal Investigator

KUBO Izumi  Faculty of Science, HIROSHIMA UNIVERSITY,Professor, 理学部, 教授 (70022621)

Co-Investigator(Kenkyū-buntansha) NAKAMURA Muneataka  Faculty of Science, HIROSHIMA UNIVERSITY,Assistant, 理学部, 助手 (10227944)
YAMATO Yuichi  Faculty of Science, HIROSHIMA UNIVERSITY,Assistant, 理学部, 助手 (70112175)
TAKENAKA Shigeo  Okayama Science University, Faculty of Science, Professor, 理学部, 教授 (80022680)
TAIRA Kazuaki  Faculty of Science, HIROSHIMA UNIVERSITY,Professor, 理学部, 教授 (90016163)
OHARU Shinnosuke  Faculty of Science, HIROSHIMA UNIVERSITY,Professor, 理学部, 教授 (40063721)
Project Period (FY) 1995 – 1996
Keywordswhite noise / generalized functional / Gaussian measure / non-linear equation / semi-group / diffusion process / random-fractal / number operator
Research Abstract

The basic spaces to describe white noise system have been constructed in several ways, each of which sets up the same spaces. Those constructions are not so direct. The organizer succeeded to introduce a direct construction of the spaces and presented the results in international conferences. By the results we can compare the similarity and distinction between Hida calculus and Malliavin calculus.
Each investigator researched along the idea of the organizer in their own field in connection with white noise system. Prof.S.Oharu investigated characterization of non-linearly perturbed semi-groups and theory of locally Lipshitz semi-groups. Prof.K.Taira studied boundary problems of integro-differential operators and corresponding to the operators. Especially, he investigated constructions of their Feller semi-groups and Markov processes. Prof.Takenaka researched constructions and characterizations of self similar stable processes. The spectra, which are effective in his discussion, are expected important roles in analysis of stable white noise system. Dr.Yamato studied stochastic analysis in the relationship with infinitesimal analysis. Dr.Nakamura researched Hausdorff dimensions and packing dimensions of random fractal sets together with Hausdorff measures.
In the beginning, our main purpose was to clarify infinite dimensional Bargmann space and Levy Laplacian. But we get important results for more basic subjects. The results are useful for research of the original theme. By the investigation of infinite dimensional partial differential operators, semi-groups and diffusion processes, we can have deeper understanding of the structure of white noise systems.
One of new developments is that we introduced a new class of generalized functions or functionals and gave characterization theorems by the collaboration with Prof.H.-H.Kuo. The class is sufficiently wide to use for applications and powerful because exponential functionals are test functionals.

  • Research Products

    (56 results)

All Other

All Publications (56 results)

  • [Publications] 久保泉: "Non-isotropic Ornstein-Uhlenbeck process and white noise analysis" Proc.of Conference on Stochastic Differential and Differentia Equations. (in press). (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 馬場良和、久保泉、高橋陽一郎: "Li-Yorke's scrambled sets have measure 0" Nonlinear Analysis,Theory and Methods. 22. 1611-1162 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 久保泉: "Weighted number operators and associated processes in white noise analysis" Infinite dimensional harmonic Analysis. 146-155 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 久保泉: "Generalized functionals in white noise analysis" Probability Theory and Mathematical Statistics,World $break Scientific. 237-243 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 久保泉,H.-H.Kuo: "A simple proof of Hida distribution characterizaiton theorem" Exploring Stochastic Laws. 243-250 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 久保泉、横井嘉孝: "Generalized functions and functionals in fluctuation" Mathematical Approach to Fluctuations II,World Scientific. 203-230 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 久保泉,H.-H.Kuo: "Finite dimensional Hida distributions" Journal of Functional Analysis. 128. 1-47 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 大春愼之助,K.Okamoto: "Nonlinear evolution operators associated with nonlinear degenerate parabolic equations" Advances in Mathematical Sciences and Applications. 7(in press). (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 大春愼之助,J.A.Goldstein,T.Takahashi: "A class of semigroups of locally Lipshitzian operators and its application to generalized Kortweg-de Vries equations" Evolution Equations and Nonlinear Problems. (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 大春愼之助: "Nonlinear perturbations of a class of integrated semigroups" Hiroshima Mathematical.Journal. 26. 433-473 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 大春愼之助: "The favard class for a nonlinear parabolic problem" Recent Developement in Evolution Equation. 1-14 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭,梅津: "Semilinear Elliptic Boundary Value Problems in Chemical Reactor Theory" in press (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "Boundary value problems,Feller semigroups and Markov processes" Lecture notes in pure and applied mathematics. 175. 421-439 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "Bifurcation for nonlinear elliptic boundary value problems" Structure of Solutions of Differential Equations. 425-456 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "Bifurcation for nonlinear elliptic boundary value problems III" Advances in Differential Equations. 1. 709-727 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "Bifurcation for nonlinear elliptic boundary value problems I" Collectanea Mathematica. 47. 207-229 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "Boundary value problems for elliptic integro-differential operators" Mathematische Zeitschrift. 22. 305-327 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "On boundary value problems of nonlinear elastostatics," Osaka Journal of Mathematics. 33. 553-583 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "The Yamabe problem and nonlinear boundary value problems" Journal of Differential Equations. 122. 316-372 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "Bifurcation for nonlinear elliptic boundary value problems II" Tokyo Journal of Mathematics. 19. 387-396 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "Boundary value problems for elliptic pseudo-differential operators" Proc.America Math.Soc.123. 2519-2528 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "On the existence of Feller semigroups with boudary conditions II" J.Func.Anal.129. 108-131 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "An index formula for the de Rham complex" Tohoku Math.J.45. 331-358 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 中村宗敬: "On dimensions and measures of statistically constructed Cantor sets" Proc.of The 25th Conference of Stochastic Process and its Applications. (in press). (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 中村宗敬: "On absolutely continuous invariant measures with respect to Hausdorff measures on self-similar sets" Hiroshima Math.J.26. 1-24 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 中村宗敬,中田寿夫: "On the Julia sets of rational functions of degree two with real two parameters" Hiroshima Mathematical Journal. 26. 253-275 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 久保泉・矢野公一: "力学系1" 岩波書店(in press), 160 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "Analytic semigroups and semilinear initial boundary value problem" Cambridge University Press, (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "London Math.Soc.Lecture Notes Series" Analytic semigroups and semilinear initial boundary value problem, (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] I.Kubo: "Non-isotropic Ornstein-Uhlenbeck process and white noise analysis" Proc.of Conference on Stochastic Differential and Differentia Equations. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] I.Kubo: "Weighted number operators and associated processes in white noise analysis" Infinite dimensional harmonic Analysis. 146-155 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] I.Kubo: "Generalized functionals in white noise analysis" Probability Theory and Mathematical Statistics, World Scientific. 237-243 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Baba, I.Kubo \& Y.Takahashi: "Li-Yorke's scrambled sets have measure 0" Nonlinear Analysis, Theory and Methods. Vol.22. 1611-1612 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] I.Kubo and H.-H.Kuo: "A simple proof of Hida distribution characterization theorem" Exploring Stochastic Laws. 243-250 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] I.Kubo and Y.Yokoi: "Generalized functions and functionals in fluctuation" Mathematical Approach to Fluctuations II, World Scientific. 203-230 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] I.Kubo and H.-H.Kuo: "Finite dimensional Hida distributions" J.Func.Anal.Vol.128. 1-47 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Oharu and K.Okamoto: "Nonlinear evolution operators associated with nonlinear degenerate parabolic equations" Advances in Mathematical Sciences and Applications. Vol.7. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Oharu, J.A.Goldstein and T.Takahashi: "A class of semigroups of locally Lipshitzian operators and its application to generalized Kortweg-de Vries equations" Evolution Equations and Nonlinear Problems. (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Oharu: "Nonlinear perturbations of a class of integrated semigroups" Hiroshima Math.J.Vol.26. 433-473 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Oharu: "The favard class for a nonlinear parabolic problem" Recent Development in Evolution Equation. 1-14 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira and K.Umezu: "Semilinear Elliptic Boundary Value Problems in Chemical Reactor Theory" (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira: "Boundary value problems, Feller semigroups and Markov processes" Lecture notes in pure and applied mathematics. Vol.175. 421-439 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira: "Bifurcation for nonlinear elliptic boundary value problems" Structure of Solutions of Differential Equations, World Scientific Publishing. 425-456 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira: "Bifurcation for nonlinear elliptic boundary value problems III" Advances in Differential Equations. Vol.1. 709-727 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira: "Bifurcation for nonlinear elliptic boundary value problems I" Collectanea Mathematica. Vol.47. 207-229 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira: "Boundary value problems for elliptic integro-differential operators" Mathematische Zeitschrift. Vol.222. 305-327 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira: "On boundary value problems of nonlinear elastostatics" Osaka Journal of Mathematics. Vol.33, No.2. 553-583 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira and K.Umezu: "Bifurcation for nonlinear elliptic boundary value problems II" Tokyo Journal of Mathematics. Vol.19, No.2. 387-396 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira: "The Yamabe problem and nonlinear boundary value problems" J.Differential Equations. Vol.122. 316-372 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira: "Boundary value problems for elliptic pseudo-differential operators" Proc.America Math.Soc.Vol.123. 2519-2528 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira: "On the existence of Feller semigroups with boundary conditions II" J.Func.Anal.Vol.129. 108-131 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira: "An index formula for the de Rham complex" Tohoku Math.J.Vol.45. 331-358 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Nakamura: "On dimensions and measures of statistically constructed Cantor sets" Proc.of The 25th Conference of Stochastic Process and its Applications. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Nakamura: "On absolutely continuous invariant measures with respect to Hausdorff measures on self-similar sets" Hiroshima Math.J.Vol.26. 1-24 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Nakamura and T.Nakata: "On the Julia sets of rational functions of degree two with real two parameters" Hiroshima Math.J.Vol.26. 253-275 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira: Analytic semigroups and semilinear initial boundary value problem. London Math.Soc.Lecture Notes Series, Vol.223, Cambridge University Press, (1995)

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

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Published: 1999-03-09  

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