Let $\{X_k: k \geqq 1\}$ be a sequence of i.i.d.rv with $E(X_i) = 0$ and $E(X_i^2) = \sigma^2, 0 < \sigma^2 < \infty$. Set $S_n = X_1 + \cdots + X_n$. Let $Y_n(t)$ be $S_k/\sigma n^\frac{1}{2}$ for $t = k/n$ and suitably interpolated elsewhere. This paper gives a generalization of a theorem of Iglehart which states weak convergence of $Y_n(t)$, conditioned to stay positive, to a suitable limiting process.
Publié le : 1976-06-14
Classification:
Conditioned limit theorem,
functional central limit theorem,
random walks,
weak convergence,
60F05,
60J15
@article{1176996098,
author = {Bolthausen, Erwin},
title = {On a Functional Central Limit Theorem for Random Walks Conditioned to Stay Positive},
journal = {Ann. Probab.},
volume = {4},
number = {6},
year = {1976},
pages = { 480-485},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996098}
}
Bolthausen, Erwin. On a Functional Central Limit Theorem for Random Walks Conditioned to Stay Positive. Ann. Probab., Tome 4 (1976) no. 6, pp. 480-485. http://gdmltest.u-ga.fr/item/1176996098/