On a non-homogeneous difference equation from probability theory

Jean-Luc Guilbault, Mario Lefebvre


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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DOI: https://doi.org/10.2478/tatra.v43i0.11