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February, 1976 An Invariance Principle for Random Walk Conditioned by a Late Return to Zero
W. D. Kaigh
Ann. Probab. 4(1): 115-121 (February, 1976). DOI: 10.1214/aop/1176996189

Abstract

Let $\{S_n: n \geqq 0\}$ denote the recurrent random walk formed by the partial sums of i.i.d. integer-valued random variables with zero mean and finite variance. Let $T = \min \{n \geqq 1: S_n = 0\}$. Our main result is an invariance principle for the random walk conditioned by the event $\lbrack T = n\rbrack$. The limiting process is identified as a Brownian excursion on [0, 1].

Citation

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W. D. Kaigh. "An Invariance Principle for Random Walk Conditioned by a Late Return to Zero." Ann. Probab. 4 (1) 115 - 121, February, 1976. https://doi.org/10.1214/aop/1176996189

Information

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

zbMATH: 0332.60047
MathSciNet: MR415706
Digital Object Identifier: 10.1214/aop/1176996189

Subjects:
Primary: 60B10
Secondary: 60F05, 60G50, 60J15, 60J65, 60K99

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 1 • February, 1976
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