Semigroup approach to birth-and-death stochastic dynamics in continuum
  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. 
Dmitri Finkelshtein, Yuri Kondratiev, Oleksandr Kutoviy
math.FA math-ph math.DS math.MP