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October 2020 Oscillation properties of expected stopping times and stopping probabilities for patterns consisting of consecutive states in Markov chains
Azer Kerimov, Abdullah Öner
Rocky Mountain J. Math. 50(5): 1709-1721 (October 2020). DOI: 10.1216/rmj.2020.50.1709

Abstract

We investigate a Markov chain with a state space 1,2,,r stopping at appearance of patterns consisting of two consecutive states. It is observed that the expected stopping times of the chain have surprising oscillating dependencies on starting positions. Analogously, the stopping probabilities also have oscillating dependencies on terminal states. In a nonstopping Markov chain the frequencies of appearances of two consecutive states are found explicitly.

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Azer Kerimov. Abdullah Öner. "Oscillation properties of expected stopping times and stopping probabilities for patterns consisting of consecutive states in Markov chains." Rocky Mountain J. Math. 50 (5) 1709 - 1721, October 2020. https://doi.org/10.1216/rmj.2020.50.1709

Information

Received: 30 December 2019; Revised: 24 February 2020; Accepted: 12 March 2020; Published: October 2020
First available in Project Euclid: 5 November 2020

zbMATH: 07274829
MathSciNet: MR4170681
Digital Object Identifier: 10.1216/rmj.2020.50.1709

Subjects:
Primary: 05C81, 60J10

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 5 • October 2020
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