Applied Mathematics Seminar

Speaker: Dr. Lijin Wang  

Lijin is an associate professor at University of Chinese Academy of Sciences. She is currently a visiting scholar at our department. 

Title: Modified equations for weakly convergent stochastic symplectic numerical methods via their generating functions

Abstract: In this talk, an approach of constructing stochastic modified equations of weak \(k+k' (k' ≥ 1)\) order apart from the k-th order weakly convergent stochastic symplectic numerical methods is introduced, using their  underlying generating functions This approach is valid for stochastic Hamiltonian systems with additive noises or multiplicative noises when the Hamiltonian functions \(Hr (p, q), r ≥ 1\), associated to the diffusion parts depend only on \(p\) or \(q\). We will show that the established modified equations are perturbed stochastic Hamiltonian systems of the original systems.