Elsevier

Information and Computation

Volume 247, April 2016, Pages 37-86
Information and Computation

Hybrid behaviour of Markov population models

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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.

Keywords

Stochastic process algebras
Stochastic concurrent constraint programming
Stochastic hybrid systems
Mean field
Fluid approximation
Weak convergence

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