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Quenched central limit theorems for random walks in random scenery

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  • Guillotin-Plantard, Nadine
  • Poisat, Julien

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.

Suggested Citation

  • Guillotin-Plantard, Nadine & Poisat, Julien, 2013. "Quenched central limit theorems for random walks in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1348-1367.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:4:p:1348-1367
    DOI: 10.1016/j.spa.2012.11.010
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    References listed on IDEAS

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    1. Castell, F. & Pradeilles, F., 2001. "Annealed large deviations for diffusions in a random Gaussian shear flow drift," Stochastic Processes and their Applications, Elsevier, vol. 94(2), pages 171-197, August.
    2. Csáki, Endre & König, Wolfgang & Shi, Zhan, 1999. "An embedding for the Kesten-Spitzer random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 283-292, August.
    3. Khoshnevisan, Davar & Lewis, Thomas M., 1998. "A law of the iterated logarithm for stable processes in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 89-121, May.
    4. Cerný, Jirí, 2007. "Moments and distribution of the local time of a two-dimensional random walk," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 262-270, February.
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    Citations

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    Cited by:

    1. Aurzada, Frank & Guillotin-Plantard, Nadine & Pène, Françoise, 2018. "Persistence probabilities for stationary increment processes," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1750-1771.
    2. Guy Cohen & Jean-Pierre Conze, 2017. "CLT for Random Walks of Commuting Endomorphisms on Compact Abelian Groups," Journal of Theoretical Probability, Springer, vol. 30(1), pages 143-195, March.

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