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July 2008 Large deviations for infinite dimensional stochastic dynamical systems
Amarjit Budhiraja, Paul Dupuis, Vasileios Maroulas
Ann. Probab. 36(4): 1390-1420 (July 2008). DOI: 10.1214/07-AOP362


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.


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Amarjit Budhiraja. Paul Dupuis. Vasileios Maroulas. "Large deviations for infinite dimensional stochastic dynamical systems." Ann. Probab. 36 (4) 1390 - 1420, July 2008.


Published: July 2008
First available in Project Euclid: 29 July 2008

zbMATH: 1155.60024
MathSciNet: MR2435853
Digital Object Identifier: 10.1214/07-AOP362

Primary: 60F10 , 60H15
Secondary: 37L55

Keywords: Brownian sheet , Freidlin–Wentzell LDP , infinite dimensional Brownian motion , large deviations , small noise asymptotics , stochastic evolution equations , Stochastic partial differential equations

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 4 • July 2008
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