2021/07/11 by Matija Vidmar, Vidmar, Matija
Biochemistry, Genetics and Molecular Biology · Business, Management and Accounting · Mathematics · #60J80 #Advanced Queuing Theory Analysis #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2107.05102
openalex publication_date 2021/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Continuous-state branching processes (CSBPs) with immigration (CBIs), stopped on hitting zero, are generalized by allowing the process governing immigration to be any Lévy 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.