Two-type linear fractional branching processes in varying environments with asymptotically constant mean matrices

2020/07/14 by Wang, Hua-Ming, Yao, Huizi
#15B48 #60J10 #60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2007.07840

Abstract

Consider two-type linear-fractional branching processes in varying environments with asymptotically constant mean matrices. Let ν be the extinction time. Under certain conditions, we show that both P(ν=n) and P(ν>n) are asymptotically the same as some functions of the products of spectral radii of the mean matrices. We also give an example for which P(ν=n) decays with various speeds such as (c)/(n(log n)²), (c)/(n^β),β>1 et al. which are very different from the ones of homogeneous multitype Galton-Watson processes.

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