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Weak convergence to fractional Brownian motion in Brownian scenery

Research paper by Wensheng Wang

Indexed on: 01 Jun '03Published on: 01 Jun '03Published in: Probability Theory and Related Fields



Abstract

 Kesten and Spitzer have shown that certain random walks in random sceneries converge to stable processes in random sceneries. In this paper, we consider certain random walks in sceneries defined using stationary Gaussian sequence, and show their convergence towards a certain self-similar process that we call fractional Brownian motion in Brownian scenery.