Résumé
Beaucoup de problèmes liés au couplage de processeurs conduisent à des équations fonctionnelles. En général, les fonctions inconnues représentent les fonctions génératrices d'un processus stationaire. Nous étudions ici un problème particulier, mais la méthode proposée est applicable à des cas très généraux de marches aléatoires à deux dimensions.
Summary
Many problems arising from the coupling of processors require the solution of functional equations. Generally, the unknown functions are the generating functions for a stationary distribution of the studied process. In this paper, a particular problem is addressed but results lead to a computationally reasonable solution which applies to very general two dimensional random walks.
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Fayolle, G., Iasnogorodski, R. Two coupled processors: The reduction to a Riemann-Hilbert problem. Z. Wahrscheinlichkeitstheorie verw Gebiete 47, 325–351 (1979). https://doi.org/10.1007/BF00535168
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DOI: https://doi.org/10.1007/BF00535168