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Derivation of mean-field equations for stochastic particle systems
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Grosskinsky, Stefan and Jatuviriyapornchai, Watthanan (2019) Derivation of mean-field equations for stochastic particle systems. Stochastic Processes and their Applications, 129 (4). pp. 1455-1475. doi:10.1016/j.spa.2018.05.006 ISSN 0304-4149.
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Official URL: https://doi.org/10.1016/j.spa.2018.05.006
Abstract
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under generic growth conditions on particle jump rates, and the limit provides a master equation for the single site dynamics of the particle system, which is a non-linear birth death chain. Conservation of mass in the particle system leads to conservation of the first moment for the limit dynamics, and to non-uniqueness of stationary distributions. Our findings are consistent with recent results on exchange driven growth, and provide a connection between the well studied phenomena of gelation and condensation.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Stochastic differential equations, Mean field theory , Stochastic processes, Differential equations, Partial | ||||||||
| Journal or Publication Title: | Stochastic Processes and their Applications | ||||||||
| Publisher: | Elsevier Science BV | ||||||||
| ISSN: | 0304-4149 | ||||||||
| Official Date: | April 2019 | ||||||||
| Dates: |
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| Volume: | 129 | ||||||||
| Number: | 4 | ||||||||
| Page Range: | pp. 1455-1475 | ||||||||
| DOI: | 10.1016/j.spa.2018.05.006 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 11 May 2018 | ||||||||
| Date of first compliant Open Access: | 15 October 2018 | ||||||||
| RIOXX Funder/Project Grant: |
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| Is Part Of: | Part of this work has been carried out during a stay at the Institut Henri Poincare - Centre Emile Borel during the trimester ’Stochastic Dynamics Out of Equilibrium’, and we are grateful for the institute’s hospitality and support | ||||||||
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