Open Access
January 2014 Path-valued branching processes and nonlocal branching superprocesses
Zenghu Li
Ann. Probab. 42(1): 41-79 (January 2014). DOI: 10.1214/12-AOP759


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. Henri Poincaré Probab. Stat. 34 (1998) 637–686] and Abraham and Delmas [Ann. Probab. 40 (2012) 1167–1211].


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Zenghu Li. "Path-valued branching processes and nonlocal branching superprocesses." Ann. Probab. 42 (1) 41 - 79, January 2014.


Published: January 2014
First available in Project Euclid: 9 January 2014

zbMATH: 1290.60085
MathSciNet: MR3161481
Digital Object Identifier: 10.1214/12-AOP759

Primary: 60J68 , 60J80
Secondary: 60H20 , 92D25

Keywords: Continuous-state branching process , immigration , nonlocal branching , path-valued branching process , solution flow , Stochastic equation , Superprocess

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 1 • January 2014
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