2009 Fiscal Year Final Research Report
Development of infinite-dimensional stochastic analysis forapplications to non-Markovian fields
| Project/Area Number |
19740043
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tohoku University |
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Principal Investigator |
HARIYA Yuu Tohoku University, 大学院・理学研究科, 准教授 (20404030)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 確率論 |
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| 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.
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