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Journal Articles Stochastic Processes and their Applications Year : 2014

Random walks in the quarter plane, discrete harmonic functions and conformal mappings

Abstract

We propose a new approach for finding discrete harmonic functions in the quarter plane with Dirichlet conditions. It is based on solving functional equations that are satisfied by the generating functions of the values taken by the harmonic functions. As a first application of our results, we obtain a simple expression for the harmonic function that governs the asymptotic tail distribution of the first exit time for random walks from the quarter plane. As another corollary, we prove, in the zero drift case, the uniqueness of the discrete harmonic function.
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Dates and versions

hal-00780452 , version 1 (24-01-2013)
hal-00780452 , version 2 (08-02-2014)

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Cite

Kilian Raschel. Random walks in the quarter plane, discrete harmonic functions and conformal mappings. Stochastic Processes and their Applications, 2014, 114 (10), pp.3147-3178. ⟨10.1016/j.spa.2014.04.013⟩. ⟨hal-00780452v2⟩
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