# Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions

Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

1 IMT - Institut de Mathématiques de Toulouse UMR5219 2 LMA-Poitiers - Laboratoire de Mathématiques et Applications

Abstract : It is classical to approximate the distribution of fractional Brownian motion by a renormalized sum $S n$ of dependent Gaussian random variables. In this paper we consider such a walk $Z n$ that collects random rewards $\xi j$ for $j \in \mathbb Z,$ when the ceiling of the walk $S n$ is located at $j.$ The random reward or scenery $\xi j$ is independent of the walk and with heavy tail. We show the convergence of the sum of independent copies of $Z n$ suitably renormalized to a stable motion with integral representation, whose kernel is the local time of a fractional Brownian motion fBm. This work extends a previous work where the random walk $S n$ had independent increments limits.

Keywords : local times Key words: stable process self-similarity fractional Brownian motion random walk random scenery local times.

Autor: Serge Cohen - Clément Dombry -

Fuente: https://hal.archives-ouvertes.fr/

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