  The rates of strong convergence for various approximation schemes are
investigated for a class of stochastic differential equations (SDEs) which
involve a random time change given by an inverse subordinator. SDEs to be
considered are unique in two different aspects: i) they contain two drift
terms, one driven by the random time change and the other driven by a regular,
non-random time variable; ii) the standard Lipschitz assumption is replaced by
that with a time-varying Lipschitz bound. The difficulty imposed by the first
aspect is overcome via an approach that is significantly different from a
well-known method based on the so-called duality principle. On the other hand,
the second aspect requires the establishment of a criterion for the existence
of exponential moments of functions of the random time change.
