洪佳林，研究员、博士生导师、国家二级教授、享受国务院政府特殊津贴专家。现任中国科学院数学与系统科学研究院副院长。主要研究方向: 动力系统保结构算法与随机偏微分方程数值方法，包括确定与随机哈密尔顿系统辛几何算法、确定与随机哈密尔顿偏微分方程多辛几何算法等。主持完成国家基金委重大项目课题、重大研究计划重点项目和集成项目等多个研究项目。在Springer出版社著名系列丛书“Lecture Notes in Mathematics”上出版专著；在 “J. Comput. Phys.” 、“J. Differential Equations”、“Math. Comput.”、 “Numer. Math.”、 “SIAM J. Numer. Anal.”、“SIAM J. Sci. Comput.”、“Stud. Math.”、“中国科学”等国际学术刊物上发表研究论文100余篇。

Plenty of numerical experiments show that stochastic symplectic methods are superior to non-symplectic ones especially in long-time computation, when applied to stochastic Hamiltonian systems. In this talk we first review some basic results on stochastic symplectic methods of stochastic Hamiltonian systems, such as the theory of stochastic generating functions, variational integrators, pseudo-symplectic methods, etc. Then we present the probabilistic superiority of stochastic symplectic methods of stochastic Hamiltonian systems via large deviations principle. (In collaboration with Dr. Chuchu Chen, Dr. Diancong Jin and Dr. Liying Sun)