Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of the stochastic contact Hamiltonian systems via structure-preserving 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 the convergent order theorem is provided, too. Numerical tests are shown to confirm the theoretical results and the usability of proposed approach.

翻译：随机接触哈密顿系统是一类重要的数学模型，可用于描述随机环境中具有奇数维度的耗散特性。本文通过保结构方法研究随机接触哈密顿系统的数值动力学。接触保结构格式由随机接触哈密顿-雅可比方程构建。我们设计了一种随机接触哈密顿-雅可比方程的通用数值逼近方法，并给出了收敛阶定理。数值实验验证了理论结果及所提方法的可用性。