Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term

• 成果类型: Article
• 署名作者: Cerrai, S; Röckner, M
• 署名单位: University of Florence; University of Bielefeld
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2004
• 页码: 1100-1139
• 关键词: partial-differential equations; perturbations

摘要

Following classical work by Freidlin [Trans. Amer Math. Soc. (1988) 305 665-657] and subsequent works by Sowers [Ann. Probab. (1992) 20 504-537] and Peszat [Probab. Theory Related Fields (1994) 98 113-136], we prove large deviation estimates for the small noise limit of systems of stochastic reaction-diffusion equations with globally Lipschitz but unbounded diffusion coefficients, however, assuming the reaction terms to be only locally Lipschitz with polynomial growth. This generalizes results of the above mentioned authors. Our results apply, in particular, to systems of stochastic Ginzburg-Landau equations with multiplicative noise.