FREIDLIN-WENTZELL LDP IN PATH SPACE FOR MCKEAN-VLASOV EQUATIONS AND THE FUNCTIONAL ITERATED LOGARITHM LAW

• 成果类型: Article
• 署名作者: dos Reis, Goncalo; Salkeld, William; Tugaut, Julian
• 署名单位: University of Edinburgh; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1416
• 发表日期: 2019
• 页码: 1487-1540
• 关键词: large deviations; propagation; THEOREM; limit

摘要

We show two Freidlin-Wentzell-type Large Deviations Principles (LDP) in path space topologies (uniform and Holder) for the solution process of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) using techniques which directly address the presence of the law in the coefficients and altogether avoiding decoupling arguments or limits of particle systems. We provide existence and uniqueness results along with several properties for a class of MV-SDEs having random coefficients and drifts of superlinear growth. As an application of our results, we establish a functional Strassen-type result (law of iterated logarithm) for the solution process of a MV-SDE.