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June, 1976 On a Functional Central Limit Theorem for Random Walks Conditioned to Stay Positive
Erwin Bolthausen
Ann. Probab. 4(3): 480-485 (June, 1976). DOI: 10.1214/aop/1176996098

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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Erwin Bolthausen. "On a Functional Central Limit Theorem for Random Walks Conditioned to Stay Positive." Ann. Probab. 4 (3) 480 - 485, June, 1976. https://doi.org/10.1214/aop/1176996098

Information

Published: June, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0336.60024
MathSciNet: MR415702
Digital Object Identifier: 10.1214/aop/1176996098

Subjects:
Primary: 60F05
Secondary: 60J15

Keywords: Conditioned limit theorem , functional central limit theorem , Random walks , weak convergence

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 3 • June, 1976
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