ON LARGE DEVIATIONS OF COUPLED DIFFUSIONS WITH TIME SCALE SEPARATION

• 成果类型: Article
• 署名作者: Puhalskii, Anatolii A.
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1043
• 发表日期: 2016
• 页码: 3111-3186
• 关键词: markov process expectations; asymptotic evaluation; invariant-measures; REGULARITY; uniqueness; PRINCIPLE; sdes

摘要

We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all of the coefficients may depend on both the slow and the fast variables and the diffusion terms may be correlated. The diffusion term in the slow process is small. A large deviation principle is obtained for the joint distribution of the slow process and of the empirical process of the fast variable. By projecting on the slow and fast variables, we arrive at new results on large deviations in the averaging framework and on large deviations of the empirical measures of ergodic diffusions, respectively. The proof relies on the property that an exponentially tight sequence of probability measures on a metric space is large deviation relatively compact. The identification of the large deviation rate function is accomplished by analyzing the large deviation limit of an exponential martingale.