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Weak convergence to fractional Brownian motion in Brownian scenery
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  • Published: June 2003

Weak convergence to fractional Brownian motion in Brownian scenery

  • Wensheng Wang1 

Probability Theory and Related Fields volume 126, pages 203–220 (2003)Cite this article

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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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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Teacher's College, Hangzhou 310012 and Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China. e-mail: wswang@mail.hz.zj.cn, , , , , , CN

    Wensheng Wang

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  1. Wensheng Wang
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Additional information

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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  • Issue Date: June 2003

  • DOI: https://doi.org/10.1007/s00440-002-0249-8

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Keywords

  • Brownian Motion
  • Weak Convergence
  • Stable Process
  • Fractional Brownian Motion
  • Gaussian Sequence
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