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A Bernoulli Excursion and Its Various Applications

Lajos Takács
Advances in Applied Probability
Vol. 23, No. 3 (Sep., 1991), pp. 557-585
DOI: 10.2307/1427622
Stable URL: http://www.jstor.org/stable/1427622
Page Count: 29
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A Bernoulli Excursion and Its Various Applications
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Abstract

This paper is concerned with a random walk process {η 0 +,η 1 +,⋯,η 2n +} in which η 2n +=η 0 +=0 and η i +≥ 0 for i=1,2,⋯ ,2n. This process is called a Bernoulli excursion. The main object is to find the distribution, the moments, and the asymptotic distribution of the random variable ω n defined by 2nω n=η 0 ++η 1 ++⋯ +η 2n +. The results derived have various applications in the theory of probability, including random graphs, tournaments and order statistics.

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