On a functional central limit theorem for random walks conditioned to stay positive

Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-23167

Bolthausen, E (1976). On a functional central limit theorem for random walks conditioned to stay positive. The Annals of Probability, 4(3):480-485.

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Abstract

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.

Item Type:	Journal Article, refereed, original work
Communities & Collections:	07 Faculty of Science > Institute of Mathematics
DDC:	510 Mathematics
Uncontrolled Keywords:	Conditioned limit theorem; functional central limit theorem; random walks; weak convergence
Language:	English
Date:	1976
Deposited On:	04 Nov 2009 14:15
Last Modified:	10 Dec 2012 14:38
Publisher:	Institute of Mathematical Statistics
ISSN:	0091-1798
Publisher DOI:	10.1214/aop/1176996098
Related URLs:	http://www.zentralblatt-math.org/zmath/en/search/?q=an:0336.60024 http://www.ams.org/mathscinet-getitem?mr=415702
WoS Citation Count:	40

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