Hybrid behaviour of Markov population models

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 p...

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Bibliographic Details
Published in:Information and computation Vol. 247; pp. 37 - 86
Main Author: Bortolussi, Luca
Format: Journal Article
Language:English
Published: Elsevier Inc 01.04.2016
Subjects:
Fluid approximation
Mean field
Stochastic concurrent constraint programming
Stochastic hybrid systems
Stochastic process algebras
Weak convergence
Mean field
Weak convergence
Stochastic process algebras
Stochastic hybrid systems
Fluid approximation
Stochastic concurrent constraint programming
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary: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.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2015.12.001