Differential equation approximations of stochastic network processes: an operator semigroup approach

Bátkai, András, Kiss, Istvan Z, Sikolya, Eszter and Simon, Péter L. (2012) Differential equation approximations of stochastic network processes: an operator semigroup approach. Networks and Heterogeneous Media, 7 (1). pp. 43-58. ISSN 1556-1801

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Abstract

The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its master equation, which is a system of linear ODEs with large state space size (N). We derive a single non-linear ODE (called mean-field approximation) for the expected value that yields a good approximation as N tends to infinity. Using only elementary semigroup theory we can prove the order O(1/N) convergence of the solution of the system to that of the mean-field equation. The proof holds also for cases that are somewhat more general than the usual density dependent one. Moreover, for Markov chains where the transition rates satisfy some sign conditions, a new approach using a countable system of ODEs for proving convergence to the mean-field limit is proposed

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Istvan Kiss
Date Deposited: 14 Nov 2012 15:38
Last Modified: 14 Nov 2012 15:38
URI: http://sro.sussex.ac.uk/id/eprint/42474
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