A functional limit theorem for stochastic integrals driven by a time-changed symmetric -stable Lévy process

Under proper scaling and distributional assumptions, we prove the convergence in the Skorokhod space endowed with the M 1 -topology of a sequence of stochastic integrals of a deterministic function driven by a time-changed symmetric α -stable Lévy process. The time change is given by the inverse β -stable subordinator.