Quenched central limit theorems for random walks in random scenery

Nadine Guillotin-Plantard and Julien Poisat

Stochastic Processes and their Applications, 2013, vol. 123, issue 4, 1348-1367

Abstract: Random walks in random scenery are processes defined by Zn:=∑k=1nωSk where S:=(Sk,k≥0) is a random walk evolving in Zd and ω:=(ωx,x∈Zd) is a sequence of i.i.d. real random variables. Under suitable assumptions on the random walk S and the random scenery ω, almost surely with respect to ω, the correctly renormalized sequence (Zn)n≥1 is proved to converge in distribution to a centered Gaussian law with explicit variance.

Keywords: Random walk in random scenery; Limit theorem; Local time (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2012.11.010

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