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.

arXiv comment20 pages, 2 figures