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The rate of strong convergence is investigated for an approximation schemefor a class of stochastic differential equations driven by a time-changedBrownian motion, where the random time changes $(E_t)_{t\ge 0}$ consideredinclude the inverses of stable and tempered stable subordinators as well astheir mixtures. Unlike those in the work of Jum and Kobayashi (2016), thecoefficients of the stochastic differential equations discussed in this paperdepend on the regular time variable $t$ rather than the time change $E_t$. Thisalteration makes it difficult to apply the method used in that paper. Toovercome this difficulty, we utilize a Gronwall-type inequality involving astochastic driver to control the moment of the error process. Moreover, inorder to guarantee that an ultimately derived error bound is finite, weestablish a useful criterion for the existence of exponential moments of powersof the random time change.

Strong approximation of stochastic differential equations driven by a time-changed Brownian motion with time-space-dependent coefficients