Conservative and Semiconservative Random Walks: Recurrence and Transience

Abramov, V 2018, 'Conservative and Semiconservative Random Walks: Recurrence and Transience', Journal of Theoretical Probability, vol. 31, no. 3, pp. 1900-1922.

Document type: Journal Article
Collection: Journal Articles

Title Conservative and Semiconservative Random Walks: Recurrence and Transience
Author(s) Abramov, V
Year 2018
Journal name Journal of Theoretical Probability
Volume number 31
Issue number 3
Start page 1900
End page 1922
Total pages 23
Publisher Springer New York LLC
Abstract In the present paper, we define conservative and semiconservative random walks in Zd 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 Zd by reduction to birth-and-death processes. We construct nontrivial examples of recurrent random walks in Zd for any d= 3 and transient random walks in Z2.
Subject Pure Mathematics not elsewhere classified
Statistics not elsewhere classified
Keyword(s) Birth-and-death process
Markovian single-server queues
Multi-dimensional random walks
DOI - identifier 10.1007/s10959-017-0747-3
Copyright notice © Springer Science+Business Media New York 2017
ISSN 0894-9840
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