Quick Search:

uzh logo
Browse by:
bullet
bullet
bullet
bullet

Zurich Open Repository and Archive

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.

[img]
Preview
PDF
421kB

View at publisher

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.

Citations

Altmetrics

Downloads

15 downloads since deposited on 04 Nov 2009
2 downloads since 12 months

Detailed statistics

Additional indexing

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 13:15
Last Modified:15 Dec 2013 21:08
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

Users (please log in): suggest update or correction for this item

Repository Staff Only: item control page