Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sojourn time in $\mathbb{Z}^+$ for the Bernoulli random walk on
  $\mathbb{Z}$   Let $(S_k)_{k\ge 1}$ be the classical Bernoulli random walk on the integer
line with jump parameters $p\in(0,1)$ 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.

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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn