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Article Dans Une Revue Journal of Applied Probability Année : 1994

Exact aggregation of absorbing Markov processes using quasi-stationary distribution

Résumé

We characterize the conditions under which an absorbing Markovian finite process (in discrete or continuous time) can be transformed into a new aggregated process conserving the Markovian property, whose states are elements of a given partition of the original state space. To obtain this characterization, a key tool is the quasi-stationary distribution associated with absorbing processes. It allows the absorbing case to be related to the irreducible one. We are able to calculate the set of all initial distributions of the starting process leading to an aggregated homogeneous Markov process by means of a finite algorithm. Finally, it is shown that the continuous time case can always be reduced to the discrete one using the uniformization technique.
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Dates et versions

hal-00852327 , version 1 (20-08-2013)

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James Ledoux, Gerardo Rubino, Bruno Sericola. Exact aggregation of absorbing Markov processes using quasi-stationary distribution. Journal of Applied Probability, 1994, 31 (3), pp.626-634. ⟨10.2307/3215143⟩. ⟨hal-00852327⟩
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