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Abstract and Applied Analysis
Volume 2017 (2017), Article ID 7189826, 7 pages
https://doi.org/10.1155/2017/7189826
Research Article

First Passage Time of a Markov Chain That Converges to Bessel Process

Mathematics Department, University of the Bahamas, Nassau, Bahamas

Correspondence should be addressed to Moussa Kounta; moc.liamg@atnuokassuom

Received 16 March 2017; Accepted 27 August 2017; Published 3 December 2017

Academic Editor: Tongxing Li

Copyright © 2017 Moussa Kounta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the probability of the first hitting time of some discrete Markov chain that converges weakly to the Bessel process. Both the probability that the chain will hit a given boundary before the other and the average number of transitions are computed explicitly. Furthermore, we show that the quantities that we obtained tend (with the Euclidian metric) to the corresponding ones for the Bessel process.