2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174892In 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 figuresProbability60G52; 60F17; 60H10; 62F10; 62M10; 86A40text