Measure-valued branching processes with immigration (Q1201891)

The paper constructs transition probabilities of a certain Markov process, called a measure-valued branching process with discrete immigration with parameter a constant. Immigration is governed by a Poisson random measure on the time-distribution space, and a probability generating function, both dependent on the parameter. As the parameter approaches 0, the immigration process approaches a continuous time, \(t>0\), Markov process, under suitable hypotheses, called a measure-valued branching process with immigration. The convergence of branching particle systems is also studied.