Geometric Methods for Stochastic Hamiltonian Dynamics

In this talk, we shall give an insight on dynamics of stochastic Hamiltonian systems from the perspective of stochastic differential equations and geometric mechanics. The report mainly includes two parts: Firstly, we will present some results of stochastic (symplectic) Hamiltonian systems with non-Gaussian Levy noise, including symplecticity, Hamilton’s principle and averaging principle. Secondly, we will introduce a stochastic version of contact Hamiltonian systems whose phase flows preserve contact structures. (This talk is based on some joint works with J. Duan, Y. Chao and Z. Wang.)