Crossings States and Sets of States in Random Walks

Vyacheslav M. Abramov ()

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-34

Abstract: Abstract We consider a random walk in $$\mathbb {Z}^2$$ Z 2 and establish a number of results for the distributions and expectations of the number of usual (undirected) and specifically defined in the paper directed state-crossings and different sets of states crossings. As well, we extend the results to d-dimensional random walks, $$d\ge 2$$ d ≥ 2 , in bounded areas.

Keywords: Simple random walks; Level-crossings and state-crossings; Undirected state-crossings; Directed state crossings; Birth-and-death processes; Markovian single-server queues; Markov fields; Branching processes; 60G50; 60J80; 60C05; 60K25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-09979-0

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