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April 2000 On the small time asymptotics of diffusion processes on Hilbert spaces
T. S. Zhang
Ann. Probab. 28(2): 537-557 (April 2000). DOI: 10.1214/aop/1019160252

Abstract

In this paper,we establish a small time large deviation principle and obtain the following small time asymptotics:

\lim_{t \to 0}2t \log P(X_0 \in B, X_t \in C) = -d^2 (B, C),

for diffusion processes on Hilbert spaces, where $d(B,C)$ is the intrinsic metric between two subsets $B$ and $C$ associated with the diffusions. The case of perturbed Ornstein–Uhlenbeck processes is treated separately at the end of the paper.

Citation

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T. S. Zhang. "On the small time asymptotics of diffusion processes on Hilbert spaces." Ann. Probab. 28 (2) 537 - 557, April 2000. https://doi.org/10.1214/aop/1019160252

Information

Published: April 2000
First available in Project Euclid: 18 April 2002

MathSciNet: MR1782266
Digital Object Identifier: 10.1214/aop/1019160252

Subjects:
Primary: 60F10 , 60H15
Secondary: 31C25

Keywords: Dirichlet form , Girsanov transform , Intrinsic metric , large deviation , stochastic evolution equation

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 2 • April 2000
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