学术报告（洪佳林 2024.9.4）

摘要：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.