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Teor. Veroyatnost. i Primenen., 2016, Volume 61, Issue 3, Pages 595–601 (Mi tvp5077)  

Short Communications

Joint statistics of random walk on $Z^1$ and accumulation of visits

J. K. Percusa, O. E. Percusb

a Courant Institute of Mathematical Sciences
b New York University

Abstract: We obtain the joint distribution $P_N(X,K |Ż)$ of the location $X$ of a one-dimensional symmetric next neighbor random walk on the integer lattice, and the number of times the walk has visited a specified site $Z$. This distribution has a simple form in terms of the one variable distribution $p_{N'} (X')$, where $N'=N-K$ and $X'$ is a function of $X$, $K$, and $Z$. The marginal distributions of $X$ and $K$ are obtained, as well as their diffusion scaling limits.

Keywords: symmetric random walks, walk on integer lattice, frequency of visits, walker visit number correlation.

DOI: https://doi.org/10.4213/tvp5077

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English version:
Theory of Probability and its Applications, 2017, 61:3, 499–505

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Received: 10.07.2015
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Citation: J. K. Percus, O. E. Percus, “Joint statistics of random walk on $Z^1$ and accumulation of visits”, Teor. Veroyatnost. i Primenen., 61:3 (2016), 595–601; Theory Probab. Appl., 61:3 (2017), 499–505

Citation in format AMSBIB
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