Random Walks in the Quarter Plane, Harmonic Functions and Conformal Mappings
نویسنده
چکیده
We propose here a new approach for finding harmonic functions of killed random walks with small steps in the quarter plane. It is based on solving a certain functional equation that satisfies the generating function 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 from the quarter plane. As another corollary, we prove, in the zero drift case, the uniqueness of the harmonic function.
منابع مشابه
Random walks in the quarter plane, discrete harmonic functions and conformal mappings
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 t...
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