Soit la somme partielle itérée, c’est à dire , où . Pour des variables aléatoires i.i.d. intégrables et de moyenne nulle, nous montrons que les probabilités de persistance satisfont
Let denote the iterated partial sums. That is, , where . Assuming are integrable, zero-mean, i.i.d. random variables, we show that the persistence probabilities
Mots clés : first passage time, iterated partial sums, persistence, lower tail probability, one-sided probability, random walk
@article{AIHPB_2013__49_3_873_0, author = {Dembo, Amir and Ding, Jian and Gao, Fuchang}, title = {Persistence of iterated partial sums}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {873--884}, publisher = {Gauthier-Villars}, volume = {49}, number = {3}, year = {2013}, doi = {10.1214/11-AIHP452}, mrnumber = {3112437}, zbl = {1274.60144}, language = {en}, url = {http://www.numdam.org/articles/10.1214/11-AIHP452/} }
TY - JOUR AU - Dembo, Amir AU - Ding, Jian AU - Gao, Fuchang TI - Persistence of iterated partial sums JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2013 SP - 873 EP - 884 VL - 49 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/11-AIHP452/ DO - 10.1214/11-AIHP452 LA - en ID - AIHPB_2013__49_3_873_0 ER -
%0 Journal Article %A Dembo, Amir %A Ding, Jian %A Gao, Fuchang %T Persistence of iterated partial sums %J Annales de l'I.H.P. Probabilités et statistiques %D 2013 %P 873-884 %V 49 %N 3 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/11-AIHP452/ %R 10.1214/11-AIHP452 %G en %F AIHPB_2013__49_3_873_0
Dembo, Amir; Ding, Jian; Gao, Fuchang. Persistence of iterated partial sums. Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 3, pp. 873-884. doi : 10.1214/11-AIHP452. http://www.numdam.org/articles/10.1214/11-AIHP452/
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