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Abstract <p>In this note we study the convergence rates of continuous-time random walks (CTRWs) to subordinated processes arising in time-fractional differential equations. Quantitative error bounds are obtained for CTRW approximations of solutions to fractional Cauchy problems, including the case of smooth diffusion coefficients of linear growth. The suggested approach relies on a probabilistic representation of the solution via an inverse stable subordinator and on a semigroup approximation principle applied to CTRWs.</p>

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Rates of Convergence of CTRWs to Generalised Fractional Evolutions

  • 期刊论文

  • 发表日期：

    2026年7月26日

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  • V. N. Kolokoltsov,
  • A. P. Sidorenko

摘要

Abstract

In this note we study the convergence rates of continuous-time random walks (CTRWs) to subordinated processes arising in time-fractional differential equations. Quantitative error bounds are obtained for CTRW approximations of solutions to fractional Cauchy problems, including the case of smooth diffusion coefficients of linear growth. The suggested approach relies on a probabilistic representation of the solution via an inverse stable subordinator and on a semigroup approximation principle applied to CTRWs.