  The rate of strong convergence is investigated for an approximation scheme
for a class of stochastic differential equations driven by a time-changed
Brownian motion, where the random time changes $(E_t)_{t\ge 0}$ considered
include the inverses of stable and tempered stable subordinators as well as
their mixtures. Unlike those in the work of Jum and Kobayashi (2016), the
coefficients of the stochastic differential equations discussed in this paper
depend on the regular time variable $t$ rather than the time change $E_t$. This
alteration makes it difficult to apply the method used in that paper. To
overcome this difficulty, we utilize a Gronwall-type inequality involving a
stochastic driver to control the moment of the error process. Moreover, in
order to guarantee that an ultimately derived error bound is finite, we
establish a useful criterion for the existence of exponential moments of powers
of the random time change.
