Towards mesoscopic ergodic theory

作     者：Weiwei Qi Zhongwei Shen Shirou Wang Yingfei Yi Weiwei Qi;Zhongwei Shen;Shirou Wang;Yingfei Yi

作者机构：Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonAB T6G 2G1Canada School of MathematicsJilin UniversityChangchun 130012China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2020年第63卷第9期

页      面：1853-1876页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 070104[理学-应用数学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：The first author was supported by China Scholarship Council.The second author was supported by University of Alberta,and Natural Sciences and Engineering Research Council of Canada(Grant Nos.RGPIN-2018-04371 and DGECR-2018-00353) The third author was supported by Pacific Institute for the Mathematical Sciences-Canadian Statistical Sciences Institute Postdoctoral Fellowship,Pacific Institute for the Mathematical Sciences-Collaborative Research Group Grant,National Natural Science Foundation of China(Grant Nos.11771026 and 11471344) the Pacific Institute for the Mathematical Sciences-University of Washington site through National Science Foundation of USA(Grant No.DMS-1712701) The fourth author was supported by Natural Sciences and Engineering Research Council of Canada Discovery(Grant No.1257749) Pacific Institute for the Mathematical Sciences-Collaborative Research Group Grant,University of Alberta,and Jilin University 

主　　题：ergodic theory stochastic di erential equation Fokker-Planck equation stationary measure physical measure mesoscopic limit 

摘      要：The present paper is devoted to a preliminary study towards the establishment of an ergodic theory for stochastic di erential equations(SDEs)with less regular coecients and degenerate *** equations are often derived as mesoscopic limits of complex or huge microscopic *** studying the associated Fokker-Planck equation(FPE),we prove the convergence of the time average of globally de ned weak solutions of such an SDE to the set of stationary measures of the FPE under Lyapunov *** the case where the set of stationary measures consists of a single element,the unique stationary measure is shown to be *** convergence results for the solutions of the FPE are established as *** of our convergence results,while being special cases of those contained in Ji et al.(2019)for SDEs with periodic coecients,have weaken the required Lyapunov conditions and are of much simpli ed *** to stochastic damping Hamiltonian systems and stochastic slow-fast systems are given.