Electronic Communications in Probability

Small time asymptotics of Ornstein-Uhlenbeck densities in Hilbert spaces

Terence Jegaraj

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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.

Article information

Electron. Commun. Probab., Volume 14 (2009), paper no. 53, 552-559.

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

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Zentralblatt MATH identifier

Primary: 60F99: None of the above, but in this section
Secondary: 60H15: Stochastic partial differential equations [See also 35R60]

small time asymptotics densities Ornstein-Uhlenbeck Hilbert space

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Jegaraj, Terence. Small time asymptotics of Ornstein-Uhlenbeck densities in Hilbert spaces. Electron. Commun. Probab. 14 (2009), paper no. 53, 552--559. doi:10.1214/ECP.v14-1510. https://projecteuclid.org/euclid.ecp/1465234762

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