内容簡介：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.

報告人：洪佳林

報告人簡介：中國科學院數學與系統科學研究院二級研究員、博士生導師。享受國務院政府特殊津貼。曾任中國科學院數學與系統科學研究院副院長、中國數學會常務理事等職。長期從事計算數學和應用數學研究工作，主要研究方向是随機和确定性動力系統的保結構算法。在SIAM系列刊物、Math.Comp.、Numer. Math.、JCP、JDE、SPA等國際學術刊物上發表研究論文100餘篇，在Springer出版社著名系列叢書Lecture Notes in Mathematics中出版學術專著三部。任《Appl. Numer. Math.》、《J. Comput. Math》等多種國際學術期刊編委。曾主持完成多項國家自然科學基金重點項目、重大研究計劃重點項目和集成項目、國際合作項目以及GF科研重點項目，曾承擔國家科技部重點研發項目和973項目任務。

時  間：2024年9月4日（周三）下午16：30開始

地  點：南海樓224數學系研習室

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2024年9月3日