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May, 1992 Random Walk Processes and their Applications in Order Statistics
Lajos Takacs
Ann. Appl. Probab. 2(2): 435-459 (May, 1992). DOI: 10.1214/aoap/1177005710


This paper is concerned with two stochastic processes, namely, a Bernoulli excursion and a tied-down random walk. Three random variables are defined for these processes, each variable representing the area of a random set determined by one of the processes. The aim is to find the distributions and the moments of these random variables and to determine their asymptotic behavior. The results derived for random walks are applied to the theory of order statistics to determine the asymptotic behavior of the moments and the distributions of two statistics which measure the deviation between two empirical distribution functions.


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Lajos Takacs. "Random Walk Processes and their Applications in Order Statistics." Ann. Appl. Probab. 2 (2) 435 - 459, May, 1992.


Published: May, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0754.62033
MathSciNet: MR1161061
Digital Object Identifier: 10.1214/aoap/1177005710

Primary: 60J15
Secondary: 60C05 , 62G30

Keywords: limit distributions , order statistics , Random walk

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.2 • No. 2 • May, 1992
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