The joint distribution of value and local time of simple random walk and reflected simple random walk

Isaac Meilijson; Yael Perlman

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arXiv · 2109.15076

The joint distribution of value and local time of simple random walk and reflected simple random walk

Isaac Meilijson·Yael Perlman

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Abstract

The joint distribution of value and local time for Brownian Motion has been reported by Borodin and Salminen. Its asymptotic behavior for recurrent random walk has been presented by Jain and Pruitt. Motivated by the need for queue size control during a pandemic (Hassin, Meilijson and Perlman), the current study presents closed form formulas for random walk and reflected random walk with $\pm 1$ increments, not necessarily fair.

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Isaac Meilijson, Yael Perlman. 2021-09-30. The joint distribution of value and local time of simple random walk and reflected simple random walk. https://arxiv.org/abs/2109.15076

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