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Measure-valued limits of interacting particle systems with k-nary interactions. II, Finite-dimensional limits
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Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2004) Measure-valued limits of interacting particle systems with k-nary interactions. II, Finite-dimensional limits. Stochastics and Stochastics Reports, Vol.76 (No.1). pp. 45-58. doi:10.1080/10451120410001661241 ISSN 1045-1129.
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Official URL: http://dx.doi.org/10.1080/10451120410001661241
Abstract
It is shown that Markov chains in Z+d describing k-nary interacting particles of d different types approximate (in the continuous state limit) Markov processes on R+d having pseudo-differential generators p (x,i (/x)) with symbols p (x,) depending polynomially (degree k) on x. This approximation can be used to prove existence and non-explosion results for the latter processes. Our general scheme of continuous state (or finite-dimensional measure-valued) limits to processes of k-nary interaction yields a unified description of these limits for a large variety of models that are intensively studied in different domains of natural science from interacting particles in statistical mechanics (e.g. coagulation-fragmentation processes) to evolutionary games and multidimensional birth and death processes from biology and social sciences.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Markov processes, Particles -- Mathematical models | ||||
Journal or Publication Title: | Stochastics and Stochastics Reports | ||||
Publisher: | Taylor & Francis | ||||
ISSN: | 1045-1129 | ||||
Official Date: | 2004 | ||||
Dates: |
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Volume: | Vol.76 | ||||
Number: | No.1 | ||||
Page Range: | pp. 45-58 | ||||
DOI: | 10.1080/10451120410001661241 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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