We propose a dynamic domain semi-Lagrangian method for stochastic Vlasov equations driven by transport noises, which arise in plasma physics and astrophysics. This method combines the volume-preserving property of stochastic characteristics with a dynamic domain adaptation strategy and a reconstruction procedure. It offers a substantial reduction in computational costs compared to the traditional semi-Lagrangian techniques for stochastic problems. Furthermore, we present the first-order convergence analysis of the proposed method, partially addressing the conjecture in the work [C.-E. Br\'{e}hier and D. Cohen, J. Comput. Dyn., 2024] on the convergence order of numerical methods for stochastic Vlasov equations. Several numerical tests are provided to show good performance of the proposed method.

翻译：本文针对等离子体物理和天体物理中由输运噪声驱动的随机Vlasov方程，提出了一种动态区域半拉格朗日方法。该方法将随机特征线的保体积特性与动态区域自适应策略及重构过程相结合，相比传统随机问题半拉格朗日技术显著降低了计算成本。此外，我们给出了所提方法的一阶收敛性分析，部分解决了[C.-E. Bréhier and D. Cohen, J. Comput. Dyn., 2024]工作中关于随机Vlasov方程数值方法收敛阶的猜想。通过若干数值实验验证了所提方法的良好性能。