Development of infinite-dimensional stochastic analysis forapplications to non-Markovian fields

• Project/Area Number: 19740043
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tohoku University
• Principal Investigator: HARIYA Yuu Tohoku University, 大学院・理学研究科, 准教授 (20404030)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥3,860,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥660,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 確率論 / 無限次元確率解析

Research Abstract

(1) I have found a path decomposition of multi-dimensional Brownian motion that relates a type of divergence formula on Wiener space obtained by myself, and Hadamard's variational formula for heat kernels of parabolic equations with Dirichlet boundary conditions.
(2) Concerning long-time asymptotics of heat kernels for parabolic equations, I have given a probabilistic explanation by means of a time-change argument which I developed in 2006, in the case where the dimension is one and associated potentials satisfy a certain integrability condition.

Research Products

• [Journal Article] Penalising Brownian Paths, volume 1969 of Lecture Notes in Math. (2009)
  • Author(s): B. Roynette, M. Yor
  • Journal Title: Springer, Berlin
• [Journal Article] Integration by parts formulae for Wiener measures restricted to subsets in R^d (2006)
  • Author(s): Y. Hariya
  • Journal Title: J. Funct. Anal. 239 Pages: 594-610
  • NAID: 120000981494
• [Journal Article] Limiting laws associated with Brownian motion perturbed by normalized exponential weights (2006)
  • Author(s): B. Roynette, P. Vallois, M. Yor
  • Journal Title: I, Studia Sci., Math., Hungar. 43 Pages: 171-246
• [Journal Article] A time-change approach to Kotani's extension of Yor's formula (2006)
  • Author(s): Y. Hariya
  • Journal Title: J. Math. Soc. Japan 58 Pages: 129-151
  • NAID: 10017178356
• [Journal Article] Conformally Invariant Processes in the Plane (2005)
  • Author(s): G.F. Lwler
  • Journal Title: Amer. Math. Soc.
• [Journal Article] Gibbs measures on Brownian paths: theory and applications (2005)
  • Author(s): V.Betz, J.Lorinzci, H. Spohn
  • Journal Title: Interacting stochastic systems(Springer) Pages: 75-102
• [Journal Article] A local criterion for smoothness of densities and application to the supremum of the Brownian sheet (1995)
  • Author(s): C. Florit, D. Nualart
  • Journal Title: Statist. Probab. Lett. 22 Pages: 25-31
• [Journal Article] Large time asymptotics for fundamental solutions of diffusion equations (1985)
  • Author(s): M. Murata
  • Journal Title: Tohoku Math. J. 37 Pages: 151-195
• [Journal Article] Hadamard's variation of the Green kernels of heat equations and their traces. (1982)
  • Author(s): S. Ozawa
  • Journal Title: I, J. Math. Soc. Japan 34 Pages: 455-473
• [Journal Article] On Edwards model for long polymer chains, II. The self-consistent potential (1981)
  • Author(s): J. Westwater
  • Journal Title: Comm. Math. Phys. 79 Pages: 53-73
• [Journal Article] On Edwards model for long polymer chains (1980)
  • Author(s): J. Westwater
  • Journal Title: Comm. Math. Phys. 72 Pages: 131-174