Path-valued branching processes and nonlocal branching superprocesses

Details Path-valued branching processes and nonlocal branching superprocesses Path-valued branching processes and nonlocal branching superprocesses

2012-03-28

arxiv.org/abs/1203.6150v1

Mathematics

Probability

37 pages

Scientific paper

A family of continuous-state branching processes with immigration are constructed as the solution flow of a stochastic equation system driven by time-space noises. The family can be regarded as an inhomogeneous increasing path-valued branching process with immigration. Two nonlocal branching immigration superprocesses can be defined from the flow. We identify explicitly the branching and immigration mechanisms of those processes. The results provide new perspectives into the tree-valued Markov processes of Aldous and Pitman [Ann. Inst. H. Poincare Probab. Statist. 34 (1998), 637--686] and Abraham and Delmas [Ann. Probab. To appear].

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