The Annals of Probability

Large deviations for infinite dimensional stochastic dynamical systems

Amarjit Budhiraja, Paul Dupuis, and Vasileios Maroulas

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Abstract

The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the process state is infinite dimensional. In this paper we show how such approximations can be avoided for a variety of infinite dimensional models driven by some form of Brownian noise. The approach is based on a variational representation for functionals of Brownian motion. Proofs of large deviations properties are reduced to demonstrating basic qualitative properties (existence, uniqueness and tightness) of certain perturbations of the original process.

Article information

Source
Ann. Probab., Volume 36, Number 4 (2008), 1390-1420.

Dates
First available in Project Euclid: 29 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.aop/1217360973

Digital Object Identifier
doi:10.1214/07-AOP362

Mathematical Reviews number (MathSciNet)
MR2435853

Zentralblatt MATH identifier
1155.60024

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60F10: Large deviations
Secondary: 37L55: Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15]

Keywords
Large deviations Brownian sheet Freidlin–Wentzell LDP stochastic partial differential equations stochastic evolution equations small noise asymptotics infinite dimensional Brownian motion

Citation

Budhiraja, Amarjit; Dupuis, Paul; Maroulas, Vasileios. Large deviations for infinite dimensional stochastic dynamical systems. Ann. Probab. 36 (2008), no. 4, 1390--1420. doi:10.1214/07-AOP362. https://projecteuclid.org/euclid.aop/1217360973


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