Limit theorems for supercritical branching processes in Markovian environment with linear fractional offspring distributions

Abstract

In this paper, we study the asymptotic behaviour for distribution of supercritical branching process in a Markovian environment with linear fractional offspring distributions. Phase transitions in the behaviour of the process is discovered, through investigating the strongly, intermediately and weakly supercritical cases.

arXiv commentCurrent version (Version 2): 35 pages (19 pages in Version 1), 1 figure (0 figure in Version 1). The limit theorem for weakly supercritical case is added. Some typos are corrected, 1 figure is added for illustration, the structure of the manuscript is improved and there is a change of authorship