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A functional limit theorem for stochastic integrals driven by a time-changed symmetric \(\alpha\)-stable Lévy process. (English) Zbl 1301.60034

Summary: 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 Lévy process. The time change is given by the inverse \(\beta\)-stable subordinator.

MSC:

60F17 Functional limit theorems; invariance principles
60H05 Stochastic integrals
60G51 Processes with independent increments; Lévy processes
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