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Distributed Markov Processes
Samy Abbes 1
(10/2011)

This paper introduces the model of Distributed Markov Processes (DMP), a probabilistic model of a system with distributed state over n>1 sites. The definition of DMP being given, the notion of stopping time in the distributed context is introduced, and a Strong Markov Property is derived. DMP are then characterized by their characteristic coefficients. These play a role similar to the coefficients of the transition matrix of discrete Markov chains, excepted that normalization conditions sufficient to define a DMP are not given here. The characteristic coefficients of a DMP are shown to satisfy the concurrency equations. The main result of the paper is the proof of the existence of DMP on n sites, n>1. The proof makes use of the tools introduced, especially the notion of stopping times. The case n=2 has been extensively studied in a previous note.
1 :  Preuves, Programmes et Systèmes (PPS)
CNRS : UMR7126 – Université Paris VII - Paris Diderot
Mathématiques/Probabilités

Informatique/Modélisation et simulation

Informatique/Réseaux et télécommunications
Markov processes – concurrency – distributed system
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