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

C. Hein; P. Imkeller; I. Pavlyukevich

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arXiv · 0811.3769

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

C. Hein·P. Imkeller·I. Pavlyukevich

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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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C. Hein, P. Imkeller, I. Pavlyukevich. 2008-11-23. Limit theorems for p-variations of solutions of SDEs driven by additive non-Gaussian stable Levy noise. https://arxiv.org/abs/0811.3769

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