Permanent URL to this publication: http://dx.doi.org/10.5167/uzh23167
Bolthausen, E (1976). On a functional central limit theorem for random walks conditioned to stay positive. The Annals of Probability, 4(3):480485.

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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.
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Additional indexing
Item Type:  Journal Article, refereed, original work 

Communities & Collections:  07 Faculty of Science > Institute of Mathematics 
Dewey Decimal Classification:  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:  05 Apr 2016 13:30 
Publisher:  Institute of Mathematical Statistics 
ISSN:  00911798 
Publisher DOI:  10.1214/aop/1176996098 
Related URLs:  http://www.zentralblattmath.org/zmath/en/search/?q=an:0336.60024 http://www.ams.org/mathscinetgetitem?mr=415702 
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