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 Rd. 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. © 2011 Elsevier Inc.
Finkelshtein, D., Kondratiev, Y., & Kutoviy, O. (2012). Semigroup approach to birth-and-death stochastic dynamics in continuum. Journal of Functional Analysis, 262(3), 1274–1308. https://doi.org/10.1016/j.jfa.2011.11.005