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Distributional properties of jumps of multi-type CBI processes
- Source :
- Electronic Journal of Probability 29, (2024), 1-39.
- Publication Year :
- 2023
-
Abstract
- We study the distributional properties of jumps of multi-type continuous state and continuous time branching processes with immigration (multi-type CBI processes). We derive an expression for the distribution function of the first jump time of a multi-type CBI process with jump size in a given Borel set having finite total L\'evy measure, which is defined as the sum of the measures appearing in the branching and immigration mechanisms of the multi-type CBI process in question. Using this we derive an expression for the distribution function of the local supremum of the norm of the jumps of a multi-type CBI process. Further, we show that if $A$ is a nondegenerate rectangle anchored at zero and with total L\'evy measure zero, then the probability that the local coordinate-wise supremum of jumps of the multi-type CBI process belongs to $A$ is zero. We also prove that a converse statement holds.<br />Comment: 55 pages. Title has been changed
- Subjects :
- Mathematics - Probability
60J80, 60G55
Subjects
Details
- Database :
- arXiv
- Journal :
- Electronic Journal of Probability 29, (2024), 1-39.
- Publication Type :
- Report
- Accession number :
- edsarx.2308.05639
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1214/24-EJP1125