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

Pengfei Xu¹ ; Jianhua Huang¹ ; Wei Yan²

¹ College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, PR China.
² College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, PR China.

Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 51.

Résumé

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.

Détail

DOI : 10.1051/mmnp/2021041

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