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

摘要

In this article we consider the asymptotic behavior of the power variation of processes of the form ∫_0~t u_(s_) dS_s~α, where S~α is an α-stable process with index of stability 0<α<2 and the integral is an Ito integral. We establish stable convergence of corresponding fluctuations. These results provide statistical tools to infer the process u from discrete observations.