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.
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Received: 17 April 2002 / Revised version: 11 October 2002 / Published online: 15 April 2003
Research supported by NSFC (10131040).
Mathematics Subject Classification (2002): 60J55, 60J15, 60J65
Key words or phrases: Weak convergence – Random walk in random scenery – Local time – Fractional Brownian motion in Brownian scenery
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Wang, W. Weak convergence to fractional Brownian motion in Brownian scenery. Probab. Theory Relat. Fields 126, 203–220 (2003). https://doi.org/10.1007/s00440-002-0249-8
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DOI: https://doi.org/10.1007/s00440-002-0249-8