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<p>This paper analyzes the Stochastic Parareal (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 bounded time intervals. We first revisit the classical parareal algorithm and SParareal algorithm. Then we investigate mean-square convergence of the SParareal algorithm based on the stochastic <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation>-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.</p>

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Stochastic parareal algorithm for stochastic differential equations

  • 期刊论文

  • 发表日期：

    2025年6月23日

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  • Huanxin Wang,
  • Junhan LYU,
  • Zicheng Peng,
  • Min Li

摘要

This paper analyzes the Stochastic Parareal (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 bounded time intervals. We first revisit the classical parareal algorithm and SParareal algorithm. Then we investigate mean-square convergence of the SParareal algorithm based on the stochastic \(\theta \) θ -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.