Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Likelihood ratio processes for Markovian particle systems with killing and jumps


Code(s) de Classification MSC:

Résumé: We consider Markov processes built from pasting together strong Markov processes which are killed at a position dependent rate and connected via a transition kernel. We give necessary and sufficient conditions for local absolute continuity of probability laws for such processes on a suitable path space and derive an explicit formula for the corresponding likelihood ratio process. The main tool is the consideration of the process between successive jumps -- what we call ``elementary experiments'' -- and criteria for absolute continuity of laws of the process there. We apply our results to systems of branching diffusions with interactions and immigrations.

Mots Clés: Particle systems ; likelihood ratio ; branching processes

Date: 1999-12-09

Prépublication numéro: PMA-551