Parameter-related strong convergence rate and polynomial stability of a Euler's type method for time-changed stochastic differential equations

A Euler's type method with the equidistant step size is proposed for a class of time-changed stochastic differential equations driven by the multiplicative noise and the strong convergence rate that is related to the parameter of the time changing process is obtained. Such a observation of the convergence rate is significantly different from those existing results that employ methods with the random step size. The polynomial stability in the mean square sense of the numerical method is also studied, which is in line with the asymptotic behavior of the underlying equation.