Research article

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

  • 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.

    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

    Related Papers:

  • 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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