标题： 随机并行算法用于随机微分方程 显示英文标题

标题： Stochastic Parareal Algorithm for Stochastic Differential Equations

摘要： 本文分析了用于随机微分方程（SDEs）的SParareal算法。 与经典Parareal算法相比，SParareal算法通过引入随机扰动加速收敛，在无限时间区间上实现线性收敛。 我们首先回顾经典Parareal算法和随机Parareal算法。 然后，基于SDEs的随机$\theta$方法，研究SParareal算法的均方稳定性，推导出在四种采样规则下的线性误差界。 数值实验表明，SParareal算法在求解线性和非线性SDEs方面具有优越性，相比经典Parareal算法减少了所需的迭代次数。 显示英文摘要

摘要： This paper analyzes the SParareal algorithm for stochastic differential equations (SDEs). Compared to the classical Parareal algorithm, the SParareal algorithm accelerates convergence by introducing stochastic perturbations, achieving linear convergence over unbounded time intervals. We first revisit the classical Parareal algorithm and stochastic Parareal algorithm. Then we investigate mean-square stability of the SParareal algorithm based on the stochastic $\theta$-method for SDEs, deriving linear error bounds under four sampling rules. Numerical experiments demonstrate the superiority of the SParareal algorithm in solving both linear and nonlinear SDEs, reducing the number of iterations required compared to the classical Parareal algorithm.