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

Published online by Cambridge University Press:  09 December 2016

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.

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2016 

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