Abstract
In the present paper, we define conservative and semiconservative random walks in \(\mathbb {Z}^d\) and study various families of random walks. The family of symmetric random walks is one of the families of conservative random walks, and simple (Pólya) random walks are their representatives. The classification of random walks given in the present paper enables us to provide a new approach to random walks in \(\mathbb {Z}^d\) by reduction to birth-and-death processes. We construct nontrivial examples of recurrent random walks in \(\mathbb {Z}^d\) for any \(d\ge 3\) and transient random walks in \(\mathbb {Z}^2\).
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19 November 2018
The aim of this note is to correct the errors in the formulation and proof of Lemma 4.1 in [1] and some claims that are based on that lemma.
19 November 2018
The aim of this note is to correct the errors in the formulation and proof of Lemma 4.1 in [1] and some claims that are based on that lemma.
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The author thanks the anonymous referee for valuable comments leading to substantial improvement of the paper.
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Abramov, V.M. Conservative and Semiconservative Random Walks: Recurrence and Transience. J Theor Probab 31, 1900–1922 (2018). https://doi.org/10.1007/s10959-017-0747-3
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DOI: https://doi.org/10.1007/s10959-017-0747-3