A Functional Limit Theorem for stochastic integrals driven by a time-changed symmetric \alpha-stable L\'evy process

TL;DR

This paper establishes a functional limit theorem for stochastic integrals driven by a time-changed symmetric alpha-stable Lévy process, showing convergence under specific scaling and distributional conditions.

Contribution

It introduces a new limit theorem for stochastic integrals with time-changed stable Lévy processes, expanding understanding of their asymptotic behavior.

Findings

Proves convergence in the Skorokhod M_1 topology.

Identifies conditions for the limit process.

Extends classical results to time-changed stable processes.

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 \alpha-stable L\'evy process. The time change is given by the inverse \beta-stable subordinator.