On a non-homogeneous difference equation from probability theory

Jean-Luc Guilbault; Mario Lefebvre

doi:10.2478/v10127-009-0027-4

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On a non-homogeneous difference equation from probability theory

Tatra Mountains Mathematical Publications

Volume 43 (2009): Issue 1 (August 2009)

By: Jean-Luc Guilbault and Mario Lefebvre

Open Access

|Nov 2012

Abstract

The so-called gambler’s ruin problem in probability theory is considered for a Markov chain having transition probabilities depending on the current state. This problem leads to a non-homogeneous difference equation with non-constant coefficients for the expected duration of the game. This mathematical expectation is computed explicitly.

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Articles in this issue

DOI: https://doi.org/10.2478/v10127-009-0027-4 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

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Language: English

Page range: 81 - 90

Published on: Nov 12, 2012

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Markov chain,

ruin problem,

Ornstein-Uhlenbeck process,

non-constant coefficients,

hypergeometric function,

reducible equation

Related subjects:

Mathematics,

General mathematics

© 2012 Jean-Luc Guilbault, Mario Lefebvre, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Volume 43 (2009): Issue 1 (August 2009)