The Annals of Probability

On the small time asymptotics of diffusion processes on Hilbert spaces

T. S. Zhang

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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.

Article information

Ann. Probab., Volume 28, Number 2 (2000), 537-557.

First available in Project Euclid: 18 April 2002

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Mathematical Reviews number (MathSciNet)

Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60F10: Large deviations
Secondary: 31C25: Dirichlet spaces

Dirichlet form intrinsic metric large deviation stochastic evolution equation Girsanov transform


Zhang, T. S. On the small time asymptotics of diffusion processes on Hilbert spaces. Ann. Probab. 28 (2000), no. 2, 537--557. doi:10.1214/aop/1019160252.

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