Small time asymptotics of Ornstein-Uhlenbeck densities in Hilbert spaces

Terence Jegaraj (University of New South Wales)

Abstract


We show that Varadhan's small time asymptotics for densities of the solution of a stochastic differential equation in $\mathbb{R}^n$ carries over to a Hilbert space-valued Ornstein-Uhlenbeck process whose transition semigroup is strongly Feller and symmetric. In the Hilbert space setting, densities are with respect to a Gaussian invariant measure.

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Pages: 552-559

Publication Date: December 9, 2009

DOI: 10.1214/ECP.v14-1510

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