Hybrid Behaviour of Markov Population Models

We investigate the behaviour of population models written in Stochastic Concurrent ConstraintProgramming (sCCP), a stochastic extension of Concurrent Constraint Programming. In particular,we focus on models from which we can define a semantics of sCCP both in terms of ContinuousTime Markov Chains (CTMC) and in terms of Stochastic Hybrid Systems, in which some populationsare approximated continuously, while others are kept discrete. We will prove the correctness of thehybrid semantics from the point of view of the limiting behaviour of a sequence of models for increasingpopulation size. More specifically, we prove that, under suitable regularity conditions, the sequence ofCTMC constructed from sCCP programs for increasing population size converges to the hybrid systemconstructed by means of the hybrid semantics. We investigate in particular what happens for sCCPmodels in which some transitions are guarded by boolean predicates or in the presence of instantaneoustransitions.