Large deviations for infinite dimensional stochastic dynamical systems

Details Large deviations for infinite dimensional stochastic dynamical systems Large deviations for infinite dimensional stochastic dynamical systems

2008-08-27

arxiv.org/abs/0808.3631v1

Annals of Probability 2008, Vol. 36, No. 4, 1390-1420

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP362 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

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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