Published in

Duke University Press, Kyoto Journal of Mathematics, 2(49), 2009

DOI: 10.1215/kjm/1256219156

Links

Tools

Export citation

Search in Google Scholar

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

Journal article published in 2009 by Serge Cohen, Clément Dombry
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

Full text: Download

Green circle
Preprint: archiving allowed
Upload
Green circle
Postprint: archiving allowed
Upload
Red circle
Published version: archiving forbidden
Policy details
Data provided by SHERPA/RoMEO

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 $ ξ_j $ for $ j 𝟄 \mathbb Z$, when the ceiling of the walk $ S_n $ is located at $ j$. The random reward (or scenery) $ ξ_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.