Continuous-state branching processes with spectrally positive migration
Probability
2022-07-06 v4
Abstract
Continuous-state branching processes (CSBPs) with immigration (CBIs), stopped on hitting zero, are generalized by allowing the process governing immigration to be any L\'evy process without negative jumps. Unlike the CBIs, these newly introduced processes do not appear to satisfy any natural affine property on the level of the Laplace transforms of the semigroups. Basic properties are noted. Explicit formulae (on neighborhoods of infinity) for the Laplace transforms of the first passage times downwards and of the explosion time are derived.
Keywords
Cite
@article{arxiv.2107.05102,
title = {Continuous-state branching processes with spectrally positive migration},
author = {Matija Vidmar},
journal= {arXiv preprint arXiv:2107.05102},
year = {2022}
}