内容简介：The stochastic Hamiltonian system is a key model across various fields such as physics, chemistry, and engineering. A defining characteristic of this system is the preservation of the stochastic symplectic structure by its phase flow. When it comes to numerically approximating the stochastic Hamiltonian system, there is an expectation that the numerical methods should preserve the symplecticity, which has driven the development of stochastic symplectic methods. These methods have demonstrated superior performance over non-symplectic counterparts in plenty of numerical experiments, especially excelling in capturing the asymptotic behaviors of the underlying solution process. In this talk, we delve into the theoretical explanations for the superiority of stochastic symplectic methods from the perspectives of the large deviation principles and the law of iterated logarithms, respectively. We prove that stochastic symplectic methods can preserve the asymptotic behaviors of the original systems over long time horizons, while non-symplectic ones do not.

报告人：洪佳林

报告人简介：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。享受国务院政府特殊津贴。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。长期从事计算数学和应用数学研究工作，主要研究方向是随机和确定性动力系统的保结构算法。在SIAM系列刊物、Math.Comp.、Numer. Math.、JCP、JDE、SPA等国际学术刊物上发表研究论文100余篇，在Springer出版社著名系列丛书Lecture Notes in Mathematics中出版学术专著三部。任《Appl. Numer. Math.》、《J. Comput. Math》等多种国际学术期刊编委。曾主持完成多项国家自然科学基金重点项目、重大研究计划重点项目和集成项目、国际合作项目以及GF科研重点项目，曾承担国家科技部重点研发项目和973项目任务。

时  间：2024年9月4日（周三）下午16：30开始

地  点：南海楼224数学系研习室

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信息科学技术学院

2024年9月3日