On the small time asymptotics of diffusion processes on Hilbert spaces
Zhang, T. S.
Ann. Probab., Tome 28 (2000) no. 1, p. 537-557 / Harvested from Project Euclid
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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.
Publié le : 2000-04-14
Classification:  Dirichlet form,  intrinsic metric,  large deviation,  stochastic evolution equation,  Girsanov transform,  60H15,  60F10,  31C25 
@article{1019160252,
     author = {Zhang, T. S.},
     title = {On the small time asymptotics of diffusion processes on Hilbert
		 spaces},
     journal = {Ann. Probab.},
     volume = {28},
     number = {1},
     year = {2000},
     pages = { 537-557},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1019160252}
}

Zhang, T. S. On the small time asymptotics of diffusion processes on Hilbert
		 spaces. Ann. Probab., Tome 28 (2000) no. 1, pp.  537-557. http://gdmltest.u-ga.fr/item/1019160252/