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2009 Small time asymptotics of Ornstein-Uhlenbeck densities in Hilbert spaces
Terence Jegaraj
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Electron. Commun. Probab. 14: 552-559 (2009). DOI: 10.1214/ECP.v14-1510


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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Terence Jegaraj. "Small time asymptotics of Ornstein-Uhlenbeck densities in Hilbert spaces." Electron. Commun. Probab. 14 552 - 559, 2009.


Accepted: 9 December 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1196.60055
MathSciNet: MR2570678
Digital Object Identifier: 10.1214/ECP.v14-1510

Primary: 60F99
Secondary: 60H15

Keywords: densities , Hilbert space , Ornstein-Uhlenbeck , small time asymptotics

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