Invariant measure of stochastic higher order KdV equation driven by Poisson processes

Abstract

The current paper is devoted to stochastic damped higher order KdV equation driven by Poisson process. We establish the well-posedness of stochastic damped higher-order KdV equation, and prove that there exists an unique invariant measure for non-random initial conditions. Some discussion on the general pure jump noise case are also provided. Some numerical simulations of the invariant measure are provided to support the theoretical results. Mathematics Subject Classification. 60H15, 37L55. Received March 27, 2020. Accepted July 13, 2021.