Limit theorem for random walk in weakly dependent random scenery

Nadine Guillotin-Plantard; Clémentine Prieur

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 4, page 1178-1194
  • ISSN: 0246-0203

Abstract

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Let S=(Sk)k≥0 be a random walk on ℤ and ξ=(ξi)i∈ℤ a stationary random sequence of centered random variables, independent of S. We consider a random walk in random scenery that is the sequence of random variables (Un)n≥0, where Un=∑k=0nξSk, n∈ℕ. Under a weak dependence assumption on the scenery ξ we prove a functional limit theorem generalizing Kesten and Spitzer’s [Z. Wahrsch. Verw. Gebiete50 (1979) 5–25] theorem.

How to cite

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Guillotin-Plantard, Nadine, and Prieur, Clémentine. "Limit theorem for random walk in weakly dependent random scenery." Annales de l'I.H.P. Probabilités et statistiques 46.4 (2010): 1178-1194. <http://eudml.org/doc/242307>.

@article{Guillotin2010,
abstract = {Let S=(Sk)k≥0 be a random walk on ℤ and ξ=(ξi)i∈ℤ a stationary random sequence of centered random variables, independent of S. We consider a random walk in random scenery that is the sequence of random variables (Un)n≥0, where Un=∑k=0nξSk, n∈ℕ. Under a weak dependence assumption on the scenery ξ we prove a functional limit theorem generalizing Kesten and Spitzer’s [Z. Wahrsch. Verw. Gebiete50 (1979) 5–25] theorem.},
author = {Guillotin-Plantard, Nadine, Prieur, Clémentine},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random walks; random scenery; weak dependence; limit theorem; local time},
language = {eng},
number = {4},
pages = {1178-1194},
publisher = {Gauthier-Villars},
title = {Limit theorem for random walk in weakly dependent random scenery},
url = {http://eudml.org/doc/242307},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Guillotin-Plantard, Nadine
AU - Prieur, Clémentine
TI - Limit theorem for random walk in weakly dependent random scenery
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 4
SP - 1178
EP - 1194
AB - Let S=(Sk)k≥0 be a random walk on ℤ and ξ=(ξi)i∈ℤ a stationary random sequence of centered random variables, independent of S. We consider a random walk in random scenery that is the sequence of random variables (Un)n≥0, where Un=∑k=0nξSk, n∈ℕ. Under a weak dependence assumption on the scenery ξ we prove a functional limit theorem generalizing Kesten and Spitzer’s [Z. Wahrsch. Verw. Gebiete50 (1979) 5–25] theorem.
LA - eng
KW - random walks; random scenery; weak dependence; limit theorem; local time
UR - http://eudml.org/doc/242307
ER -

References

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