Year: 2014
Type: article
Abstract: 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].
Source: The Annals of Probability
DOI: 10.1214/12-aop759
Author: Zenghu Li
Institution: Beijing Normal University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2081725032