Path-valued branching processes and nonlocal branching superprocesses
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 Poincar\'{e} Probab. Stat. 34 (1998) 637-686] and Abraham and Delmas [Ann. Probab. 40 (2012) 1167-1211].
Cite
@article{arxiv.1203.6150,
title = {Path-valued branching processes and nonlocal branching superprocesses},
author = {Zenghu Li},
journal= {arXiv preprint arXiv:1203.6150},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AOP759 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)