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

Shang Wu; Pengfei Xu; Jianhua Huang; Shang Wu; Pengfei Xu; Jianhua Huang

doi:10.3934/math.2020457

AIMS Mathematics

2020, Volume 5, Issue 6: 7145-7160. doi: 10.3934/math.2020457

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Research article

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

College of Liberal Arts and Science, National University of Defense Technology, Changsha, 410073, P. R. China

Received: 22 July 2020 Accepted: 30 August 2020 Published: 10 September 2020
MSC : 60H15; 37A25

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.
- stochastic Ostrovsky equation,
- pure jump process,
- invariant measure,
- ergodicity
Citation: Shang Wu, Pengfei Xu, Jianhua Huang. Invariant measure of stochastic damped Ostrovsky equation driven by pure jump noise[J]. AIMS Mathematics, 2020, 5(6): 7145-7160. doi: 10.3934/math.2020457

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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.

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