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

Hein, C.; Imkeller, P.; Pavlyukevich, I.

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

Authors

Hein, C.

Imkeller, P.

Pavlyukevich, I.

Description

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.
16 pages, 3 figures