Geodesic
Limit theorem for perturbed random walks
Teoriâ slučajnyh processov, Tome 24 (2019) no. 2, pp. 61-78

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider random walks perturbed at zero which behave like (possibly different) random walk with independent and identically distributed increments on each half lines and restarts at $0$ whenever they cross that point. We show that the perturbed random walk, after being rescaled in a proper way, converges to a skew Brownian motion whose parameter is defined by renewal functions of the simple random walk and the transition probabilities from $0$.
Keywords: Invariance principle, Reflected Brownian motion, Renewal function, Skew Brownian motion. 
@article{THSP_2019_24_2_a4,
     author = {Hoang-Long Ngo and Marc Peign\'e},
     title = {Limit theorem for perturbed random walks},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {61--78},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2019_24_2_a4/}
}
TY  - JOUR
AU  - Hoang-Long Ngo
AU  - Marc Peigné
TI  - Limit theorem for perturbed random walks
JO  - Teoriâ slučajnyh processov
PY  - 2019
SP  - 61
EP  - 78
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2019_24_2_a4/
LA  - en
ID  - THSP_2019_24_2_a4
ER  - 
%0 Journal Article
%A Hoang-Long Ngo
%A Marc Peigné
%T Limit theorem for perturbed random walks
%J Teoriâ slučajnyh processov
%D 2019
%P 61-78
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2019_24_2_a4/
%G en
%F THSP_2019_24_2_a4
Hoang-Long Ngo; Marc Peigné. Limit theorem for perturbed random walks. Teoriâ slučajnyh processov, Tome 24 (2019) no. 2, pp. 61-78. http://geodesic.mathdoc.fr/item/THSP_2019_24_2_a4/