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Limit Theorems for Continuous-Time Branching Flows

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  19 February 2016

Hui He  and
Rugang Ma
Hui He*
Affiliation:
Beijing Normal University
Rugang Ma*
Affiliation:
Central University of Finance and Economics
*
∗ Postal address: Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People's Republic of China. Email address: hehui@bnu.edu.cn.
∗∗ Postal address: School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081, People's Republic of China. Email address: marugang@mail.bnu.edu.cn.
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Abstract

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We construct a flow of continuous-time and discrete-state branching processes. Some scaling limit theorems for the flow are proved, which lead to the path-valued branching processes and nonlocal branching superprocesses, over the positive half line, studied in Li (2014).

Keywords

Stochastic flowbranching processcontinuous timesuperprocessdiscrete statenonlocal branching

MSC classification

Primary: 60J68: Superprocesses
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60G57: Random measures
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 2 , June 2014 , pp. 317 - 332
Copyright
© Applied Probability Trust 

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