Hybrid behaviour of Markov population models

TitleHybrid behaviour of Markov population models
Publication TypeJournal Article
Year of PublicationIn Press
AuthorsBortolussi L
JournalInformation and Computation
Keywordsfluid approximation, Mean field, stochastic concurrent constraint programming, stochastic hybrid systems, Stochastic process algebras, Weak convergence

Abstract We investigate the behaviour of population models, specified in stochastic Concurrent Constraint Programming (sCCP). In particular, we focus on models from which we can define a semantics both in terms of Continuous Time Markov Chains (CTMC) and in terms of Stochastic Hybrid Systems, in which some populations are approximated continuously, while others are kept discrete. We will prove the correctness of the hybrid semantics from the point of view of the limiting behaviour of a sequence of models for increasing population size. More specifically, we prove that, under suitable regularity conditions, the sequence of \{CTMC\} constructed from sCCP programs for increasing population size converges to the hybrid system constructed by means of the hybrid semantics. We investigate in particular what happens for sCCP models in which some transitions are guarded by boolean predicates or in the presence of instantaneous transitions.