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- W3100682593 abstract "Let $(S_k)_{kge 1}$ be the classical Bernoulli random walk on the integer line with jump parameters $pin(0,1)$ and $q=1-p$. The probability distribution of the sojourn time of the walk in the set of non-negative integers up to a fixed time is well-known, but its expression is not simple. By modifying slightly this sojourn time--through a particular counting process of the zeros of the walk as done by Chung & Feller [On fluctuations in coin-tossings, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 605-608]-, simpler representations may be obtained for its probability distribution. In the aforementioned article, only the symmetric case ($p=q=1/2$) is considered. This is the discrete counterpart to the famous Paul L'evy's arcsine law for Brownian motion." @default.
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- W3100682593 date "2012-01-01" @default.
- W3100682593 modified "2023-09-26" @default.
- W3100682593 title "Sojourn time in ℤ+for the Bernoulli random walk on ℤ" @default.
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- W3100682593 doi "https://doi.org/10.1051/ps/2010013" @default.
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