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A note on two-level superprocesses

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Wen-Ming Hong
Wen-Ming Hong*
Affiliation:
Beijing Normal University
*
∗ Postal address: Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China. Email address: [email protected]
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Abstract

We prove some central limit theorems for a two-level super-Brownian motion with random immigration, which lead to limiting Gaussian random fields. The covariances of those Gaussian fields are explicitly characterized.

Keywords

Super-Brownian motiontwo-level superprocessrandom immigrationcentral limit theorem

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. 202 - 210
Copyright
Copyright © Applied Probability Trust 2004 

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References

Dawson, D. A. (1977). The critical measure diffusion process. Z. Wahrscheinlichkeitsth 40, 125–145.CrossRefGoogle Scholar
Dawson, D. A., and Hochberg, K. J. (1991). A multilevel branching model. Adv. Appl. Prob. 23, 701–715.CrossRefGoogle Scholar
Dawson, D. A., and Perkins, E. A. (1991). Historical Process (Memoirs Amer. Math. Soc. 454). American Mathematical Society, Providence, RI.Google Scholar
Dawson, D. A., Gorostiza, L. G., and Li, Z. H. (2002). Non-local branching superprocesses and some related models. Acta Appl. Math. 74, 93–112.CrossRefGoogle Scholar
Dawson, D. A., Gorostiza, L. G., and Wakolbinger, A. (2001). Occupation time fluctuations in branching systems. J. Theoret. Prob. 14, 729–796.Google Scholar
Gorostiza, L. G., Hochberg, K. J., and Wakolbinger, A. (1995). Persistence of a critical super-2 process. J. Appl. Prob. 32, 534–540.CrossRefGoogle Scholar
Hong, W. M. (2002). Longtime behavior for the occupation time of super-Brownian motion with random immigration. Stoch. Process. Appl. 102, 43–62.Google Scholar
Hong, W. M., and Li, Z. H. (1999). A central limit theorem for the super-Brownian motion with super-Brownian immigration. J. Appl. Prob. 36, 1218–1224.Google Scholar
Iscoe, I. A. (1986). Weighted occupation time for a class of measure-valued branching processes. Prob. Theory Relat. Fields 71, 85–116.Google Scholar
Wu, Y. (1992). Dynamic particle systems and multilevel measure branching processes. Doctoral Thesis, Carleton University.Google Scholar
Wu, Y. (1994). Asymptotic behavior of the two level measure branching process. Ann. Prob. 22, 854–874.Google Scholar