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