A Central Limit Theorem for Two-Dimensional Random Walks in Random Sceneries

Bolthausen, Erwin

Ann. Probab., Tome 17 (1989) no. 4, p. 108-115 / Harvested from Project Euclid

Résumé

Let $S_n, n \in \mathbb{N}$, be a recurrent random walk on $\mathbb{Z}^2 (S_0 = 0)$ and $\xi(\alpha), \alpha \in \mathbb{Z}^2$, be i.i.d. $\mathbb{R}$-valued centered random variables. It is shown that $\sum^n_{i = 1}\xi(S_i)/ \sqrt{n \log n}$ satisfies a central limit theorem. A functional version is presented.

Publié le : 1989-01-14
Classification: Random walk, random scenery, central limit theorem, 60F05, 60J15, 60K35

@article{1176991497,
     author = {Bolthausen, Erwin},
     title = {A Central Limit Theorem for Two-Dimensional Random Walks in Random Sceneries},
     journal = {Ann. Probab.},
     volume = {17},
     number = {4},
     year = {1989},
     pages = { 108-115},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991497}
}

Bolthausen, Erwin. A Central Limit Theorem for Two-Dimensional Random Walks in Random Sceneries. Ann. Probab., Tome 17 (1989) no. 4, pp.  108-115. http://gdmltest.u-ga.fr/item/1176991497/