Some properties of continuous-state branching processes, with applications to Bartoszyński’s virus model. (English) Zbl 0562.92015
The paper is concerned with R. Bartoszyński’s rabies model [Math. Biosciences 24, 355-377 (1975; Zbl 0324.92028)] which is well-known to be a particular case of a continuous-state branching process. A one-one correspondence with compound Poisson processes is obtained and used to obtain various limit theorems for the population size and the jump times. A particular interesting feature is the existence of a last jump time T, and the asymptotics include limit results conditionally upon \(T>t\).
Reviewer: S.Asmussen
MSC:
92D25 | Population dynamics (general) |
60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
60J85 | Applications of branching processes |