Measure-valued discrete branching Markov processes

Beznea, Lucian; Lupaşcu, Oana

doi:10.1090/tran/6514

Measure-valued discrete branching Markov processes
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Trans. Amer. Math. Soc. 368 (2016), 5153-5176 Request permission

Abstract:

We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing kernel. In particular, we may start with a superprocess, obtaining a branching process with state space the finite configurations of positive finite measures on a topological space. A main tool in proving the path regularity of the branching process is the existence of convenient superharmonic functions having compact level sets, allowing the use of appropriate potential theoretical methods.

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