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Large deviations for super-Brownian motion with immigration

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  14 July 2016

Mei Zhang
Mei Zhang*
Affiliation:
Beijing Normal University and Central University of Finance and Economics
*
∗ Postal address: Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China. Email address: zhangmei212@sina.com
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Abstract

We derive a large-deviation principle for super-Brownian motion with immigration, where the immigration is governed by the Lebesgue measure. We show that the speed function is t 1/2 for d = 1, t/logt for d = 2 and t for d ≥ 3, which is different from that of the occupation-time process counterpart (without immigration) and the model of random immigration.

Keywords

Large-deviation principlesuper-Brownian motionmeasure-valued processesimmigration processes

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 41 , Issue 1 , March 2004 , pp. 187 - 201
Copyright
Copyright © Applied Probability Trust 2004 

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