<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

On a non-homogeneous difference equation from probability theory

D´epartement de math´ematiques et de g´enie industriel École Polytechnique C.P. 6079, Succursale Centre-ville Montréal, Qu´ebec H3C 3A7 CANADA

D´epartement de math´ematiques et de génie industriel École Polytechnique C.P. 6079, Succursale Centre-ville Montréal, Qu´ebec H3C 3A7 CANADA

Tatra Mountains Mathematical Publications

{"article-title":"On a non-homogeneous difference equation from probability theory"}

The so-called gambler’s ruin problem in probability theory is considered for a Markov chain having transition probabilities depending on the current state....

On a non-homogeneous difference equation from probability theory

Published Online: Nov 12, 2012

Page range: 81 - 90

DOI: https://doi.org/10.2478/v10127-009-0027-4

Keywords
Markov chain, ruin problem, Ornstein-Uhlenbeck process, non-constant coefficients, hypergeometric function, reducible equation

This content is open access.

On a non-homogeneous difference equation from probability theory

Published Online: Nov 12, 2012

Page range: 81 - 90

DOI: https://doi.org/10.2478/v10127-009-0027-4

KeywordsMarkov chain, ruin problem, Ornstein-Uhlenbeck process, non-constant coefficients, hypergeometric function, reducible equation

This content is open access.

Keywords
Markov chain, ruin problem, Ornstein-Uhlenbeck process, non-constant coefficients, hypergeometric function, reducible equation