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

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

2008-11-23

arxiv.org/abs/0811.3769v1

Mathematics

Probability

16 pages, 3 figures

Scientific paper

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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