Abstract

This talk will first give a new criterion on the existence of invariant measures for stochastic Hamiltonian systems with relaxation damping and possibly bounded potential force and unbounded random force. The criteria on their exponential ergodicity, large deviation principles of Donsker and Varadhan, moderate deviation principles and Freidlin-Wentzell type asymptotic measure concentration theorem are presented. One of the key techniques are to construct better Lyapunov functions based on Wu liming’s theory on stochastic damping Hamiltonian systems. The results are applied to well-known stochastic van der Pol equation, stochastic van der Pol-Duffing equation and a series of stochastic relaxing oscillation systems.