Let $\{S_n: n \geqq 0\}$ denote the recurrent random walk formed by the partial sums of i.i.d. integer-valued random variables with zero mean and finite variance. Let $T = \min \{n \geqq 1: S_n = 0\}$. Our main result is an invariance principle for the random walk conditioned by the event $\lbrack T = n\rbrack$. The limiting process is identified as a Brownian excursion on [0, 1].
Publié le : 1976-02-14
Classification:
Conditioned limit theorems,
hitting time,
invariance principle,
random walk,
weak convergence,
60B10,
60G50,
60J15,
60K99,
60F05,
60J65
@article{1176996189,
author = {Kaigh, W. D.},
title = {An Invariance Principle for Random Walk Conditioned by a Late Return to Zero},
journal = {Ann. Probab.},
volume = {4},
number = {6},
year = {1976},
pages = { 115-121},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996189}
}
Kaigh, W. D. An Invariance Principle for Random Walk Conditioned by a Late Return to Zero. Ann. Probab., Tome 4 (1976) no. 6, pp. 115-121. http://gdmltest.u-ga.fr/item/1176996189/