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Occupation time processes of super-Brownian motion with cut-off branching

Part of: General theory in ordinary differential equations Markov processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Zhao Dong  and
Shui Feng
Zhao Dong*
Affiliation:
Chinese Academy of Sciences
Shui Feng*
Affiliation:
McMaster University
*
∗ Postal address: Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, PR China. Email address: dzhao@mail.amt.ac.cn
∗∗ Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada. Email address: shuifeng@mcmail.cis.mcmaster.ca
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Abstract

In this article we investigate a class of superprocess with cut-off branching, studying the long-time behavior of the occupation time process. Persistence of the process holds in all dimensions. Central-limit-type theorems are obtained, and the scales are dimension dependent. The Gaussian limit holds only when d ≤ 4. In dimension one, a full large deviation principle is established and the rate function is identified explicitly. Our result shows that the super-Brownian motion with cut-off branching in dimension one has many features that are similar to super-Brownian motion in dimension three.

Keywords

Super-Brownian motionoccupation time processlarge deviation

MSC classification

Primary: 60F10: Large deviations 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 34A34: Nonlinear equations and systems, general
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 984 - 997
Copyright
Copyright © Applied Probability Trust 2004 

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Footnotes

Supported by the Natural Science Foundation of China and the Natural Science and Engineering Research Council of Canada.

Supported by the Natural Science and Engineering Research Council of Canada.

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