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Article Dans Une Revue Journal of Theoretical Probability Année : 2015

An Increment-Type Set-Indexed Markov Property

Résumé

We present and study a Markov property, named C-Markov, adapted to processes indexed by a general collection of sets. This new definition fulfils one important expectation for a set-indexed Markov property: there exists a natural generalization of the concept of transition operator which leads to characterization and construction theorems of C-Markov processes. Several usual Markovian notions, including Feller and strong Markov properties, are also developed in this framework. Actually, the C-Markov property turns out to be a natural extension of the two-parameter *-Markov property to the multiparameter and the set-indexed settings. Moreover, extending a classic result of the real-parameter Markov theory, sample paths of multiparameter C-Feller processes are proved to be almost surely right-continuous. Concepts and results presented in this study are illustrated with various examples.
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Dates et versions

hal-01291633 , version 1 (21-03-2016)

Identifiants

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Paul Balança. An Increment-Type Set-Indexed Markov Property. Journal of Theoretical Probability, 2015, 28 (4), pp.1271-1310. ⟨10.1007/s10959-014-0555-y⟩. ⟨hal-01291633⟩
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