2020/09/26 by Foucart, Clément, Ma, Chunhua, Yuan, Linglong
#60F15 #FOS: Mathematics #Probability (math.PR) #primary 60J80 #secondary 60F05
paper · doi:10.48550/arxiv.2009.12564
We prove and extend some results stated by Mark Pinsky: Limit theorems for continuous state branching processes with immigration [Bull. Amer. Math. Soc. 78(1972), 242--244]. Consider a continuous-state branching process with immigration (Yt,t≥ 0) with branching mechanism Ψ and immigration mechanism Φ (CBI(Ψ,Φ) for short). We shed some light on two different asymptotic regimes occurring when ∫0(Φ(u))/(|Ψ(u)|)du