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<p>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.</p>

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Stochastic Conformal Integrators for Linearly Damped Stochastic Poisson Systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月2日

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  • Charles-Edouard Bréhier,
  • David Cohen,
  • Yoshio Komori

摘要

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.