Pierre Del Moral; Shulan Hu*; Liming Hu, Moderate deviations for interacting processes; Statistica Sinica, 2015.
【学术期刊】《Statistica Sinica》，2015年第3期。
【作者简介】胡淑兰，4556银河国际教授，博士生导师。文澜青年学者，青年教师“科研新星”。主要从事概率统计、大数据统计、经济计量学、随机算法理论及其应用等方面的研究。在《Bernoulli》《Statistics Sinica》《Stochastic Processes and their applications》《Science in China》等国内外权威学术期刊发表论文二十余篇，独撰学术专著一本，主编“十四五”全国统计规划教材一本。主持国家自然科学基金青年项目、国家社会科学基金一般项目、中央高校课题、研究生精品课程建设、全英文课程建设项目、企事业单位横向课题等十几项。指导学生荣获市场调查大赛、美国数学建模大赛等各类比赛一二等奖。
【主要观点】This article is concerned with moderate deviation principles of a class of interacting empirical processes. We derive an explicit description of the rate function, and we illustrate these results with Feynman-Kac particle models arising in nonlinear filtering, statistical machine learning, rare event analysis, and computational physics. We discuss functional moderate deviations of the occupation measures for both the strong τ-topology on the space of finite and bounded measures as well as for the corresponding stochastic processes on some class of functions equipped with the uniform topology, yielding the first results of this type for mean field interacting processes. Our approach is based on an original semigroup analysis combined with Orlicz norm inequalities, stochastic perturbation techniques, and projective limit large deviation methods.
