Numerical integrations of stochastic contact Hamiltonian systems via stochastic contact Hamilton–Jacobi equation

Abstract

Stochastic contact Hamiltonian systems are an important class of mathematical models, which can describe the dissipative properties with odd dimensions in random scenario. In this article, we investigate the dynamics of the systems via structure-preserving numerical methods. The contact structure-preserving schemes are constructed by the stochastic contact Hamilton–Jacobi equation. A general numerical approximation method of the stochastic contact Hamilton–Jacobi equation is devised, and convergence order theorem is provided. Numerical tests are shown to confirm the theoretical results and the advantages of proposed approach.