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
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
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