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Ornstein-Uhlenbeck type processes and branching processes with immigration

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Zeng-Hu Li
Zeng-Hu Li*
Affiliation:
Beijing Normal University
*
∗Postal address: Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China. Email address: lizh@email.bnu.edu.cn
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Abstract

It is shown that an Ornstein-Uhlenbeck type process associated with a spectrally positive Lévy process can be obtained as the fluctuation limits of both discrete state and continuous state branching processes with immigration.

Keywords

Branching processimmigrationLévy processOrnstein-Uhlenbeck type processfluctuation limit

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 627 - 634
Copyright
Copyright © Applied Probability Trust 2000 

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Footnotes

Research supported by the National Natural Science Foundation of China (Grant No. 19361060).

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