Limit theorems for p-variations of solutions of SDEs driven by additive non-Gaussian stable Levy noise

2008/11/23 by Hein, C., Imkeller, P., Pavlyukevich, I.
#60F17 #60G52 #60H10 #62F10 #62M10 #86A40 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0811.3769

Abstract

In this paper we study the asymptotic properties of the power variations of stochastic processes of the type X=Y+L, where L is an alpha-stable Levy process, and Y a perturbation which satisfies some mild Lipschitz continuity assumptions. We establish local functional limit theorems for the power variation processes of X. In case X is a solution of a stochastic differential equation driven by L, these limit theorems provide estimators of the stability index alpha. They are applicable for instance to model fitting problems for paleo-climatic temperature time series taken from the Greenland ice core.

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