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Semigroup approach to birth-and-death stochastic dynamics in continuum (1109.5094v2)
Published 23 Sep 2011 in math.FA, math-ph, math.DS, and math.MP
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 $\mathbb{R}d$. 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.