The Annals of Probability

Large deviations for infinite dimensional stochastic dynamical systems

Amarjit Budhiraja, Paul Dupuis, and Vasileios Maroulas

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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

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

First available in Project Euclid: 29 July 2008

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Zentralblatt MATH identifier

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]

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


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.

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