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A central limit theorem for super-Brownian motion with super-Brownian immigration

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Wen-Ming Hong  and
Zeng-Hu Li
Wen-Ming Hong*
Affiliation:
Fudan University
Zeng-Hu Li*
Affiliation:
Beijing Normal University
*
∗Postal address: Department of Mathematics, Fudan University, Shanghai 200433, Peoples Republic of China. Email address: [email protected]
∗∗Postal address: Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China. Email address: [email protected].
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Abstract

We prove a central limit theorem for the super-Brownian motion with immigration governed by another super-Brownian. The limit theorem leads to Gaussian random fields in dimensions d ≥ 3. For d = 3 the field is spatially uniform; for d ≥ 5 its covariance is given by the potential operator of the underlying Brownian motion; and for d = 4 it involves a mixture of the two kinds of fluctuations.

Keywords

Super-Brownian motionimmigrationrandom mediumcentral limit theorem

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F05: Central limit and other weak theorems
Type
Short Communications
Information
Journal of Applied Probability , Volume 36 , Issue 4 , December 1999 , pp. 1218 - 1224
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

This research supported by the National Natural Science Foundation of China (Grant No. 19361060 and Grant No. 19671011) and the Mathematical Center of the State Education Commission.

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