Truncated Euler-Maruyama method for time-changed stochastic differential equations with super-linear state variables and H\"older's continuous time variables

TL;DR

This paper introduces a new explicit numerical method for solving non-autonomous time-changed stochastic differential equations with super-linear growth and H"older continuous time variables, proving its strong convergence and demonstrating its effectiveness through simulations.

Contribution

The paper develops a truncated Euler-Maruyama method tailored for a class of complex stochastic differential equations with super-linear and H"older continuous coefficients, establishing its convergence properties.

Findings

The method achieves strong convergence in finite time intervals.

Convergence rate of the method is rigorously established.

Numerical simulations confirm the theoretical results.

Abstract

An explicit numerical method is developed for a class of non-autonomous time-changed stochastic differential equations, whose coefficients obey H\"older's continuity in terms of the time variables and are allowed to grow super-linearly in terms of the state variables. The strong convergence of the method in the finite time interval is proved and the convergence rate is obtained. Numerical simulations are provided.