Semigroup approach to birth-and-death stochastic dynamics in continuum

2011/09/30 by Dmitri Finkelshtein, Yuri Kondratiev, Oleksandr Kutoviy · 2 citations
Mathematics · Physics and Astronomy · #math-ph #math.DS #math.FA #math.MP #msc:35Q83 #msc:46E30 #msc:47D06 #msc:82C21

paper · pdf

published as Journal of Functional Analysis, 2012, 262(3), p. 1274-1308 · 35 pages

arxiv created 2011/10/16 · arxiv updated 2015/01/27

Abstract

We describe a general approach to the construction of a state evolution corresponding to the Markov generator of a spatial birth-and-death dynamics in ℝ^d. We present conditions on the birth-and-death intensities which are sufficient for the existence of an evolution as a strongly continuous semigroup in a proper Banach space of correlation functions satisfying the Ruelle bound. The convergence of a Vlasov-type scaling for the corresponding stochastic dynamics is considered.

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