Moderate deviation principles for weakly interacting particle systems

• 成果类型: Article
• 署名作者: Budhiraja, Amarjit; Wu, Ruoyu
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0723-3
• 发表日期: 2017
• 页码: 721-771
• 关键词: fluctuations; limit; REPRESENTATIONS; probabilities; propagation; Tightness; DYNAMICS; chaos; MODEL

摘要

Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas the second describes a collection of pure jump Markov processes with a countable state space. For both cases the moderate deviation principle is formulated in terms of a large deviation principle (LDP), with an appropriate speed function, for suitably centered and normalized empirical measure processes. For the first family of models the LDP is established in the path space of an appropriate Schwartz distribution space whereas for the second family the LDP is proved in the space of (the Hilbert space of square summable sequences)-valued paths. Proofs rely on certain variational representations for exponential functionals of Brownian motions and Poisson random measures.