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

TL;DR

This paper investigates the asymptotic behavior of power variations of stochastic processes driven by non-Gaussian stable Levy noise, providing limit theorems that help estimate the stability index alpha, with applications in climate data modeling.

Contribution

It establishes local functional limit theorems for power variations of processes driven by stable Levy noise, including solutions to SDEs, aiding in parameter estimation.

Findings

Derived limit theorems for power variations of L-stable driven processes.

Provided methods to estimate the stability index alpha from data.

Applied results to paleo-climatic temperature series modeling.

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.