The Annals of Probability
- Ann. Probab.
- Volume 36, Number 4 (2008), 1390-1420.
Large deviations for infinite dimensional stochastic dynamical systems
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.
Ann. Probab., Volume 36, Number 4 (2008), 1390-1420.
First available in Project Euclid: 29 July 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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]
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