December 2016 Distributions of jumps in a continuous-state branching process with immigration
Xin He, Zenghu Li
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J. Appl. Probab. 53(4): 1166-1177 (December 2016).

Abstract

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.

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Xin He. Zenghu Li. "Distributions of jumps in a continuous-state branching process with immigration." J. Appl. Probab. 53 (4) 1166 - 1177, December 2016.

Information

Published: December 2016
First available in Project Euclid: 7 December 2016

zbMATH: 1356.60132
MathSciNet: MR3581249

Subjects:
Primary: 60H20 , 60J80

Keywords: branching process , continuous state , immigration , jump size , jump time , maximal jump

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 4 • December 2016
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