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

Abstract

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 Œ±-stable Lévy process. The time change is given by the inverse Œ≤-stable subordinator.