Power variation for Itô integrals with respect to α-stable processes

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Abstract

In this article we consider the asymptotic behavior of the power variation of processes of the form inline image, where Sα is an α-stable process with index of stability 0<α<2 and the integral is an Itô integral. We establish stable convergence of corresponding fluctuations. These results provide statistical tools to infer the process u from discrete observations.

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