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<p>Under partial dissipativity and super-linear growth conditions on the coefficients, we investigate the numerical approximation of random periodic solutions for McKean-Vlasov stochastic differential equations. By combining reflection coupling with the continuous-time backward Euler–Maruyama scheme on an infinite-time horizon, we establish the existence and uniqueness in distribution of numerical random periodic solutions. We further derive discretization error bounds on the infinite-time horizon, which yield the convergence rate of the backward Euler–Maruyama approximation to the random periodic solution in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation>-Wasserstein distance. The results show that the convergence of the numerical random periodic solutions is improved by taking a smaller step size and a larger number of particles.</p>

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Error Bounds of Random Periodic Solutions for McKean–Vlasov Stochastic Differential Equations

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Min Zhu,
  • Hongshuai Dai,
  • Mingtian Tang

摘要

Under partial dissipativity and super-linear growth conditions on the coefficients, we investigate the numerical approximation of random periodic solutions for McKean-Vlasov stochastic differential equations. By combining reflection coupling with the continuous-time backward Euler–Maruyama scheme on an infinite-time horizon, we establish the existence and uniqueness in distribution of numerical random periodic solutions. We further derive discretization error bounds on the infinite-time horizon, which yield the convergence rate of the backward Euler–Maruyama approximation to the random periodic solution in the \(L^{1}\) L 1 -Wasserstein distance. The results show that the convergence of the numerical random periodic solutions is improved by taking a smaller step size and a larger number of particles.