Explicit numerical method for highly non-linear time-changed stochastic differential equations

An explicit numerical method is developed for a class of time-changed stochastic differential equations, whose the coefficients obey Hölder’s continuity in terms of the time variable and are allowed to grow super-linearly in terms of the state variable. The strong convergence of the method in a finite time interval is proved and the convergence rate is obtained. Numerical simulations are provided, which are in line with those theoretical results.

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