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Differential equation approximations of stochastic network processes: an operator semigroup approach
journal contribution
posted on 2023-06-08, 13:40 authored by András Bátkai, Istvan Kiss, Eszter Sikolya, Péter L. SimonThe 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
History
Publication status
- Published
Journal
Networks and Heterogeneous MediaISSN
1556-1801Publisher
American Institute of Mathematical Sciences (AIMS)External DOI
Issue
1Volume
7Page range
43-58Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-11-14Usage metrics
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