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Distributions of jumps in a continuous-state branching process with immigration

Part of: Markov processes Stochastic analysis

Published online by Cambridge University Press:  09 December 2016

Xin He  and
Zenghu Li
Xin He*
Affiliation:
Beijing Normal University
Zenghu Li*
Affiliation:
Beijing Normal University
*
* Postal address: School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China.
* Postal address: School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China.
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Abstract

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We study the distributional properties of jumps in a continuous-state branching process with immigration. In particular, a representation is given for the distribution of the first jump time of the process with jump size in a given Borel set. From this result we derive a characterization for the distribution of the local maximal jump of the process. The equivalence of this distribution and the total Lévy measure is then studied. For the continuous-state branching process without immigration, we also study similar problems for its global maximal jump.

Keywords

Branching processcontinuous stateimmigrationmaximal jumpjump timejump size

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60H20: Stochastic integral equations
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 4 , December 2016 , pp. 1166 - 1177
Copyright
Copyright © Applied Probability Trust 2016 

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