2024年12月04日 星期三 登录 EN

学术活动
A new class of splitting methods that preserve ergodicity and exponential integrability for stochastic Langevin equation
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报告人:
Fengshan Zhang, Doctor, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
题目:
A new class of splitting methods that preserve ergodicity and exponential integrability for stochastic Langevin equation
时间地点:
16:00-17:00 November 13 (Wednesday), Z305
摘要:

In this talk, we propose a new class of splitting methods to solve the stochastic Langevin equation, which can simultaneously preserve the ergodicity and exponential integrability of the original equation. The central idea is to extract a stochastic subsystem that possesses the strict dissipation from the original equation, which is inspired by the inheritance of the Lyapunov structure for obtaining the ergodicity. We prove that the exponential moment of the numerical solution is bounded, thus validating the exponential integrability of the proposed methods. Further, we show that under moderate verifiable conditions, the methods have the first-order convergence in both strong and weak senses, and we present several concrete splitting schemes based on the methods. The splitting strategy of methods can be readily extended to construct conformal symplectic methods and high-order methods that preserve both the ergodicity and the exponential integrability, as demonstrated in numerical experiments. Our numerical experiments also show that the proposed methods have good performance in the long-time simulation. This work was completed in collaboration with Chuchu Chen, Tonghe Dang and Jialin Hong.