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2015 The mean number of sites visited by a random walk pinned at a distant point
Kôhei Uchiyama
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Electron. Commun. Probab. 20: 1-9 (2015). DOI: 10.1214/ECP.v20-4027

Abstract

This paper concerns the number $Z_n$ of sites visited up to time $n$ by a random walk $S_n$ having zero mean and moving on the two dimensional square lattice ${\bf Z}^2$. Asymptotic evaluation of the conditional expectation of $Z_n$ for large $n$ given that $S_n=x$ is carried out under some exponential moment condition. It gives an explicit form of the leading term valid uniformly in $(x, n)$, $|x|< cn$ for each $c>0$.

Citation

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Kôhei Uchiyama. "The mean number of sites visited by a random walk pinned at a distant point." Electron. Commun. Probab. 20 1 - 9, 2015. https://doi.org/10.1214/ECP.v20-4027

Information

Accepted: 24 February 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1325.60070
MathSciNet: MR3320405
Digital Object Identifier: 10.1214/ECP.v20-4027

Subjects:
Primary: 60J65
Secondary: 60J45

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