Istituto di Scienza e Tecnologie dell'Informazione     
Bortolussi L., Gast N. Mean field approximation of imprecise population processes. QUANTICOL Technical Report TR-QC-07-2015. Technical report, 2015.
We consider stochastic population processes in presence of uncertainty, originating from lack of knowledge of parameters or by unpredictable e ects of the environment. We set up a formal framework for imprecise population processes, where some parameters are allowed to vary in time within a given domain, but with no further constraint. We then consider the limit behaviour of these systems for an in nite population size, proving it is given by a di erential inclusion constructed from the (imprecise) drift. We discuss also the steady state behaviour of such a mean eld approximation. Finally, we discuss di erent approaches to compute bounds of the so-obtained di erential inclusions, proposing an e ective control-theoretic method based on Pontryagin principle for transient bounds. In the paper, we discuss separately the simpler case of models with a more constrained form of imprecision, in which lack of knowledge on parameter values allows us to assess that they belong to a given interval, albeit being constant in time. Such uncertain population models are amenable of simpler forms of analysis. The theoretical results are accompanied by an in-depth analysis of a simple epidemic model.
Subject Mean-field
B.8.2 PERFORMANCE AND RELIABILITY. Performance Analysis and Design Aids
60Jxx Markov processes

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