Large deviations for infinite dimensional stochastic dynamical systems

• 成果类型: Article
• 署名作者: Budhiraja, Amarjit; Dupuis, Paul; Maroulas, Vasileios
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; Brown University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP362
• 发表日期: 2008
• 页码: 1390-1420
• 关键词: partial-differential equations; multiplicative noise; perturbations

摘要

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.