Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations

TL;DR

This paper introduces a truncated Euler-Maruyama method for approximating non-autonomous SDEs with super-linear growth and H"older continuity, proving strong convergence and extending results to highly non-linear time-changed SDEs.

Contribution

It develops a novel truncated EM scheme for complex SDEs and establishes its strong convergence, including for time-changed equations, advancing numerical methods in stochastic analysis.

Findings

Proves strong convergence of the truncated EM method.

Establishes convergence rate for non-autonomous SDEs.

Extends convergence results to highly non-linear time-changed SDEs.

Abstract

The truncated Euler-Maruyama (EM) method is proposed to approximate a class of non-autonomous stochastic differential equations (SDEs) with the H\"older continuity in the temporal variable and the super-linear growth in the state variable. The strong convergence with the convergence rate is proved. Moreover, the strong convergence of the truncated EM method for a class of highly non-linear time-changed SDEs is studied.