Parameter-related strong convergence rates of Euler-type methods for time-changed stochastic differential equations

2025/10/18 by Ruchun Zuo, Zuo, Ruchun
#math.NA #cs.NA #math.PR

paper · pdf · doi:10.48550/arxiv.2510.16405

Abstract

An Euler-type framework with equidistant step sizes is proposed for a class of time-changed stochastic differential equations.We establish the strong convergence rate of the standard Euler--Maruyama method under the global Lipschitz condition.The theoretical analysis is then extended to the truncated Euler--Maruyama method, proving its strong convergence under relaxed Khasminskii-type conditions.Under suitable conditions, the strong convergence orders are explicitly shown to be close to α/2, where α∈ (0,1) is the parameter of the time-change process.These results are significantly different from existing works using random step sizes, which typically preserve the classical convergence order of 1/2.Numerical simulations are provided to demonstrate the theoretical findings.

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