Journal
JOURNAL OF APPLIED PROBABILITY
Volume 53, Issue 4, Pages 1166-1177Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jpr.2016.72
Keywords
Branching process; continuous state; immigration; maximal jump; jump time; jump size
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Funding
- National Natural Science Foundation of China [11131003, 11531001]
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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 Levy 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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