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A large deviation principle for a Brownian immigration particle system

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Mei Zhang
Mei Zhang*
Affiliation:
Beijing Normal University
*
∗Postal address: School of Mathematical Science, Beijing Normal University, Beijing, 100875, P. R. China. Email address: [email protected]
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Abstract

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We derive a large deviation principle for a Brownian immigration branching particle system, where the immigration is governed by a Poisson random measure with a Lebesgue intensity measure.

Keywords

Large deviation principleBrownian particle systemimmigration process

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 42 , Issue 4 , December 2005 , pp. 1120 - 1133
Copyright
© Applied Probability Trust 2005 

References

Conway, J. B. (1978). Functions of One Complex Variable. Springer, New York.CrossRefGoogle Scholar
Cox, J. T. and Griffeath, D. (1985). Occupation times for critical branching Brownian motions. Ann. Prob. 13, 1108–1132.CrossRefGoogle Scholar
Dawson, D. A. (1993). Measure-valued Markov processes. In École d'Été de Probabilités de Saint-Flour XXI (Lecture Notes. Math. 1541), Springer, Berlin, pp. 1–260.Google Scholar
Dembo, A. and Zeitouni, O. (1998). Large Deviations Techniques and Applications. Springer, New York.Google Scholar
Deuschel, J. D. and Rosen, J. (1998). Occupation time large deviations for critical branching Brownian motion, super-Brownian motion and related processes. Ann. Prob. 26, 602–643.CrossRefGoogle Scholar
Deuschel, J. D. and Wang, K. M. (1994). Large deviations for the occupation time functional of a Poisson system of independent Brownian particles. Stoch. Process. Appl. 52, 183–209.Google Scholar
Hong, W. M. (2003). Large deviations for the super-Brownian motion with super-Brownian immigration. J. Theoret. Prob. 16, 899–922.Google Scholar
Iscoe, I. and Lee, T. Y. (1993). Large deviations for occupation times of measure-valued branching Brownian motions. Stoch. Stoch. Reports 45, 177–209.Google Scholar
Kamin, S. and Peletier, L. A. (1985). Singular solutions of the heat equation with absorption. Proc. Amer. Math. Soc. 95, 205–210.Google Scholar
Lee, T. Y. (1993). Some limit theorems for super-Brownian motion and semilinear differential equations. Ann. Prob. 21, 979–995.CrossRefGoogle Scholar
Li, Z. H. (1998). Immigration processes associated with branching particle systems. Adv. Appl. Prob. 30, 657–675.Google Scholar
Widder, D. V. (1941). The Laplace Transform. Princeton University Press.Google Scholar
Zhang, M. (2004a). Large deviations for super-Brownian motion with immigration. J. Appl. Prob. 41, 187–201.Google Scholar
Zhang, M. (2004b). Moderate deviation for super-Brownian motion with immigration. Sci. China Ser. A 47, 440–452.CrossRefGoogle Scholar