Stochastic Symplectic Methods of Stochastic Hamiltonian Systems


主讲人:洪佳林 中国科学院数学与系统科学研究院研究员




主讲人介绍:洪佳林,中国科学院数学与系统科学研究院二级研究员、博士生导师,国家数学天元基金领导小组成员。曾任中国科学院数学与系统科学研究院副院长、中国数学会常务理事等职。从事计算数学和应用数学研究,主要研究方向是随机和确定性动力系统的保结构算法。在SINUM、SISC、Math. Comput.、Numer. Math.、JCP、JDE、SPA等国际学术刊物上发表研究论文100余篇,在Springer出版社系列丛书Lecture Notes in Mathematics中出版学术专著两部。曾获教育部自然科学二等奖。

内容介绍: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 variational integrators, pseudo-symplectic methods, numerical ergodicity and invariant measures, etc. Then we characterize the probabilistic superiority of stochastic symplectic methods of stochastic Hamiltonian systems via large deviations principle of numerical observables and errors.