Symplectic Integration of Stochastic Hamiltonian Systems

Jialin Hong is a professor at the Chinese Academy of Sciences. He obtained his Ph.D. in 1994 at Jilin University. He works in various directions including structure-preserving algorithms for dynamical systems involving symplectic and multi-symplectic methods for Hamiltonian ODEs and PDEs, Lie group methods and applications, numerical dynamics including chaos, bifurcations for discrete systems, numerical methods for stochastic ordinary differential systems, stochastic partial differential equations and backward stochastic differential equations, almost periodic dynamical systems, and ergodic theory. Liying Sun is a postdoctoral researcher in the Chinese Academy of Sciences. She works in stochastic differential equations and their numerical methods. She has been investigating regularity properties and strong convergence of numerical approximations for stochastic partial differential equations, weak convergence and numerical longtime behaviors of numerical approximations for stochastic partial differential equations, structure-preserving numerical methods including symplectic integrators and energy-preserving integrators for stochastic Hamiltonian system.

Chapter 1 Deterministic Hamiltonian System.- Chapter 2 Stochastic Hamiltonian System.- Chapter 3 Stochastic Structure Preserving Numerical Integrators.- Chapter 4 Stochastic Modified Equation and Its Applications.- Chapter 5 Stochastic Hamiltonian Partial Differential Equation.