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

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

## 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.

## 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.

## Altmetrics

Detailed statistics

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Conditioned limit theorem; functional central limit theorem; random walks; weak convergence English 1976 04 Nov 2009 13:15 05 Apr 2016 13:30 Institute of Mathematical Statistics 0091-1798 https://doi.org/10.1214/aop/1176996098 http://www.zentralblatt-math.org/zmath/en/search/?q=an:0336.60024http://www.ams.org/mathscinet-getitem?mr=415702

 Preview
Filetype: PDF
Size: 421kB
View at publisher

## TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.