Invariant measure of stochastic damped Ostrovsky equation driven by pure jump noise

Abstract

This paper is devoted to the stochastic damped Ostrovsky equation driven by pure jump noise. The uniformly bounded of solutions in $H^1(\mathbb{R})$ and $L^2(\mathbb{R})$ space are established respectively, which are the key tools to obtain the existence of invariant measure. By applying the convergence in measure in Hilbert space, we prove that the invariant measure is unique if the initial value is non-random. Some numerical simulation are provided to support the theoretical results.

Keywords

• stochastic ostrovsky equation
• pure jump process
• invariant measure
• ergodicity