Spatial birth-and-death Markov processes

We will consider lattice and continuous-space birth-and-death Markov dynamics. The underlying Markov process is obtained as a unique solution to a certain stochastic integral equation. The existence and uniqueness theorem as well as martingale characterization, the existence of an invariant distribution, recurrence properties and maximal irreducible measure will be discussed. We will also talk about shape results in continuous-space settings.