We propose and study conformal integrators for linearly damped stochastic Poisson systems. We analyse the qualitative and quantitative properties of these numerical integrators: preservation of dynamics of certain Casimir and Hamiltonian functions, almost sure bounds of the numerical solutions, and strong and weak rates of convergence under appropriate conditions. These theoretical results are illustrated with several numerical experiments on, for example, the linearly damped free rigid body with random inertia tensor or the linearly damped stochastic Lotka--Volterra system.

翻译：本文提出并研究了适用于线性阻尼随机泊松系统的保形积分器。我们分析了这些数值积分器的定性与定量性质：特定卡西米尔函数与哈密顿函数动力学的保持性、数值解的几乎必然有界性，以及在适当条件下的强收敛与弱收敛速率。这些理论结果通过多个数值实验得到验证，例如具有随机惯性张量的线性阻尼自由刚体系统及线性阻尼随机Lotka--Volterra系统。