• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Probability Theory and Its Interface

Research Project

Project/Area Number 09304022
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

TAKAHASHI Youichiro  Research Institutef for Mathematical Sciences, Kyoto University, Professor, 数理解析研究所, 教授 (20033889)

Co-Investigator(Kenkyū-buntansha) TANIGUCHI Setsuo  Kyushu University, Independent Graduate School of Mathematics, Associate Professor, 大学院・数理学研究科, 助教授 (70155208)
MATSUMOTO Hiroyuki  Nagoya University, School of Informatics and Sciences, Associate Professor, 情報文化部, 助教授 (00190538)
SHIGEKAWA Ichiro  Graduate School of Science, Kyoto University, Professor, 大学院・理学研究科, 教授 (00127234)
KUSUOKA Shigeo  The University of Tokyo, Graduate School of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (00114463)
FUNAKI Tadahisa  The University of Tokyo, Graduate School of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (60112174)
熊谷 隆  京都大学, 大学院・情報学研究科, 助教授 (90234509)
小倉 幸雄  佐賀大学, 理工学部, 教授 (00037847)
高信 敏  金沢大学, 理学部, 助教授 (40197124)
濱名 裕治  九州大学, 大学院・数理学研究科, 助教授 (00243923)
樋口 保成  神戸大学, 理学部, 教授 (60112075)
Project Period (FY) 1997 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥21,700,000 (Direct Cost: ¥21,700,000)
Fiscal Year 1999: ¥4,800,000 (Direct Cost: ¥4,800,000)
Fiscal Year 1998: ¥7,600,000 (Direct Cost: ¥7,600,000)
Fiscal Year 1997: ¥9,300,000 (Direct Cost: ¥9,300,000)
Keywordshydrodynamic limit / Wieener functional / Dirichlet form / large deviation and entropies / fractals / asymptotic behavior of spectrum / random walk and Brownian motion / innovation problem and noises / エントロピー / 大偏差原理 / 確率過程 / 確率解析 / 漸近挙動 / エルゴード性 / スペクトル / データ圧縮
Research Abstract

During these three years we achieved the expected results in various areas in probability theory and contributed to promote a few new directions for the future as follows.
In stochastic analysis we have made, among others, two remarkable progresses. One is the study of inequalities and their role in the analysis of function spaces on infinite dimensional, Wiener space led by Aida and Shigekawa. The other is the study of asymptotic behaviors for the Wiener functionals of exponential type by Taniguchi, Matsumoto et al. Besides them, we should mention on the trend to generalize the stochastic analysis based on the Dirichlet space theory shown, for instance, in the work of Osada.
In the theory of hydrodynamic limit Funaki, Uchiyama and thier pupil attacked more realistic models successfully and reached to the promissing problem to compare and synthesize their results with the results obtained in the Dirichlet space theory mentioned above.
In ergodic theory and its around the most remarkable progress was made in the study of the decay of correlation functions by Morita. The summer school in 1997 in this area influenced the information theory people and Han made a large deviation theory for coding.
The renewal of the classical theories and techniques was one of the slogans of the project, which was also successful as is shown by Kumagai on analysis on fractals, Atsuji on Nevalinna theory, Hamana on random walk functionals and Shirai et al. on the spetrum of graph.
Moreover, Nagai et al. applied stochastic control techniques to mathematical finance and Sugita, Takanobu et al. contributed to quasi-random nember theory by using Weyltransformation.
We owed much to PE S. Watanabe to have organized a summer school in 1999 on the noise problem. Also we owed much to the modification on the international exchange under the grant-in-aids by JSPS which has brought more fruitful results.

Report

(4 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report
  • Research Products

    (40 results)

All Other

All Publications (40 results)

  • [Publications] Y.Hamana: "The fluctuation result for the multiple point range of two-dimensional recurrent random"Ann. Probab.. 25.2. 598-639 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T.Funaki: "Motion by mean curvatur from the Ginzburg-Londau ∇ Φ Inerface model"Commun. Math. Phys.. 185.1. 1-36 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Taniguchi: "Analytic functions, Canchy formula, and stationaty phase on a real abstrct Wiener space"J. Funct. Anal.,. 143・2. 470-528 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A.Aida: "Differential Calculus on Path and Loop Spaces II Irredkucibility of Direchler Forms on"Bull. Sci. Math.. 122・8. 635-666 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N.Ikeda and H.Matsumoto: "Brownian Motion on the Hyperbolic Plane and Selberg Trace Formula"J. Funct. Anal.,. 163・1. 63-110 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Osada and H.Spohn: "Gibbs measures relative to Brownian motions"H. Psada and H. Spohn.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 重川 一郎: "確率解析(岩波講座現代数学の展開)"岩波書店. 192 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 高橋 陽一郎: "実関数とFourier解析2"岩波書店. 218 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Hamana: "The fluctuation result for the multiple point range of two-dimensional recurrent random walks"Ann. Probab.. 25(2). 598-639 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Funaki: "Motion by mean curvature from the Ginzburg-Landau∇ φ interface model"Commun. Math. Phys.. 185(1). 1-36 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Taniguchi: "Analytic functions, Canchy formula, and stationaty phase on a real abstract Wiener space"J. Funct. Analy.. 143(2). 470-528 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Aida: "Differential Calculus on Path and Loop Spaces II Irreducibility of Dirichlet Forms on Loop Spaces"Bull. Sci. Math.. 122(8). 635-666 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N. Ikeda and H. Matsumoto: "Brownian Motion on the Hyperbolic Plane and Selberg Trace Formula"J. Funct. Anal.. 163(1). 63-110 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Osada and H. Spohn: "Gibbs measures relative to Brownian motions"in J. Ann. Prob.. (to appear). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] I.Shigekawa: "Stochastic calculus"Iwanami Syoten (in Japanese). 1998

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Takahashi: "Real function and Fourier analysis 2"Iwanami Syoten (in Japanese). 1998

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] B.M.Hambly and T.Kumagai: "Transition density estimates for diffusion processes on p.c.f.self-similar fractals"Proc.London Math.Soc.. 78・3. 431-458 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Sugita and S.Takanobu: "A limit theorem for Weyl transformation in infinite-dimensional torus and central limit theorem for correlated multiple Wiener integrals"J.Math.Sci.The University of Tokyo (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Kusuoka and N.Yoshida: "Malliavin Calculus,Geometric Mixing,and Expansion of Diffusion Functionals"Prob.Theory Rel.Fields (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Osada and H.Spohn: "Gibbs measures relative to Brownian motions"J.Ann.Prob.(to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Matsumoto and N.Ueki: "Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclideam spare"J.Math.Soc.Japan (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Higuchi and T.Shirai: "The spectrum of magnetic Schrodinger operators on a graph with periodic structure"J.Funct.Anal.. 169・2. 456-480 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 長井英生: "確率微分方程式"共立出版. 240 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 小谷眞一(共著): "微分方程式と固有関数展開(現代数学の基礎)"岩波書店. 218 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Shigeki AIDA: "DIFFERENTIAL CALCULUS ON PATH AND LOOP SPACES II IRREDUCIBILITY OF DIRICHLET FORMS ON LOOP SPACES" Bulletin des Science Mathematiques. 122・8. 635-666 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiroshi SUGITA: "Limit theorem for symmetric symmetric statistics with respect to Weyl Transformation: Disappearance of Dependency (with Satoshi TAKANOBU)" Journal of Mathematics of Kyoto University. 38・4. 653-671 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Piotr BILER: "Fractal Burgers equations (with Tadahisa FUNAKI)" Journal of Differential Equations. 148・1. 9-46 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Nobuyuki IKEDA: "Brownian Motion on the Hyperbolic Plane and Selberg Trace Formula" Journal of Functional Analysis (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] Yuji HAMANA: "The fluctuation result for the multiple point range of two-dimensional recurrent random walks" The Annals of Probability. 25・2. 598-639 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Shoumei LI: "CONVERGENCE OF SET VALUED SUB- AND SUPERMARTINGALES IN THE KURATOWSKI-MOSCO SENSE (with Yukio OGURA)" The Annals of Probability. 26・3. 1384-1402 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 重川一郎: "確率解析 (岩波講座現代数学の展開)" 岩波書店, 192 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 小谷眞一: "測度と確率1.2 (岩波講座現代数学の基礎)" 岩波書店, 350 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Funaki,T.: "Motion by mean curvature from the Ginzburg-Landau ∇ φ interface model." Commun.Math.Phys.185. 1-36 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Ikeda,N.: "Short Time Asymtotics for Fundamental Solutions of Heat Equations with Boundary Conditions" New Trends in Stochastic Analysis. 182-219 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Shiga,T.: "Exponential decay rate of survival probability in a disastrous random environment" Probab.Theory.Ralat.Fields. 108. 417-439 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Atsuji,A.: "A remark on a limiting behaviour of the occupation times on unbounded domains of Brownian motion." Jour.Math.Sci.Univ.Tokyo.

    • Related Report
      1997 Annual Research Report
  • [Publications] Higuchi,Y.: "Level set representation for Gibhs states and magnetic field processes." Trends In Probability and Related Analysis,Proceedings of SAP'96. 167-175 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Taniguchi: "Analytic functions,Canchy formula,and stationary phase on a real abstract Wiener space" Journal of Functional Analysis. 143.No.2. (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 高橋陽一郎: "実関数とFourier解析1" 岩波書店, 192 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 高橋陽一郎: "実関数とFourier解析2" 岩波書店, 218 (1998)

    • Related Report
      1997 Annual Research Report

URL: 

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

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi