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. ISSN 1045-1129

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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
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of 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
Date:	2004
Volume:	Vol.76
Number:	No.1
Page Range:	pp. 45-58
Identification Number:	10.1080/10451120410001661241
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/39177

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