Nous considérons une marche aléatoire unidimensionnelle en environnement aléatoire qui est transiente à gauche. Cette marche est modifiée par des cookies qui induisent une dérive vers la droite. Le nombre de cookies par site est i.i.d. et indépendant de l'environnement. Des critères pour la récurrence et la transience de la marche sont obtenus. Pour cela, nous utilisons des processus de branchement sous-critiques en environnement aléatoire avec immigration et nous formulons des critères de récurrence et de transience pour ces processus.
We consider a left-transient random walk in a random environment on that will be disturbed by cookies inducing a drift to the right of strength 1. The number of cookies per site is i.i.d. and independent of the environment. Criteria for recurrence and transience of the random walk are obtained. For this purpose we use subcritical branching processes in random environments with immigration and formulate criteria for recurrence and transience for these processes.
Mots clés : excited random walk in a random environment, cookies of strength 1, recurrence, transience, subcritical branching process in a random environment with immigration
@article{AIHPB_2013__49_3_638_0, author = {Bauernschubert, Elisabeth}, title = {Perturbing transient random walk in a random environment with cookies of maximal strength}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {638--653}, publisher = {Gauthier-Villars}, volume = {49}, number = {3}, year = {2013}, doi = {10.1214/12-AIHP479}, mrnumber = {3112429}, zbl = {1274.60254}, language = {en}, url = {http://www.numdam.org/articles/10.1214/12-AIHP479/} }
TY - JOUR AU - Bauernschubert, Elisabeth TI - Perturbing transient random walk in a random environment with cookies of maximal strength JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2013 SP - 638 EP - 653 VL - 49 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/12-AIHP479/ DO - 10.1214/12-AIHP479 LA - en ID - AIHPB_2013__49_3_638_0 ER -
%0 Journal Article %A Bauernschubert, Elisabeth %T Perturbing transient random walk in a random environment with cookies of maximal strength %J Annales de l'I.H.P. Probabilités et statistiques %D 2013 %P 638-653 %V 49 %N 3 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/12-AIHP479/ %R 10.1214/12-AIHP479 %G en %F AIHPB_2013__49_3_638_0
Bauernschubert, Elisabeth. Perturbing transient random walk in a random environment with cookies of maximal strength. Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 3, pp. 638-653. doi : 10.1214/12-AIHP479. http://www.numdam.org/articles/10.1214/12-AIHP479/
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