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. Gebiete 50 (1979) 5–25] theorem.
Publié le : 2010-11-15
Classification:
Random walks,
Random scenery,
Weak dependence,
Limit theorem,
Local time,
60F05,
60G50,
62D05,
37C30,
37E05
@article{1288878342,
author = {Guillotin-Plantard, Nadine and Prieur, Cl\'ementine},
title = {Limit theorem for random walk in weakly dependent random scenery},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {46},
number = {1},
year = {2010},
pages = { 1178-1194},
language = {en},
url = {http://dml.mathdoc.fr/item/1288878342}
}
Guillotin-Plantard, Nadine; Prieur, Clémentine. Limit theorem for random walk in weakly dependent random scenery. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp. 1178-1194. http://gdmltest.u-ga.fr/item/1288878342/