Electronic Communications in Probability

Small time asymptotics of Ornstein-Uhlenbeck densities in Hilbert spaces

Terence Jegaraj

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465234762

Digital Object Identifier
doi:10.1214/ECP.v14-1510

Mathematical Reviews number (MathSciNet)
MR2570678

Zentralblatt MATH identifier
1196.60055

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

Keywords
small time asymptotics densities Ornstein-Uhlenbeck Hilbert space

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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References

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