Truncated Euler-Maruyama Method for Time-Changed Stochastic Differential Equations with Super-Linear State Variables and Hölder’s Continuous Time Variables

Abstract

An explicit numerical method is developed for a class of non-autonomous time-changed stochastic differential equations, whose coefficients obey Hölder’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.