Limit theorems for supercritical MBPRE with linear fractional offspring distributions

Wenming Hong; Minzhi Liu; Vladimir Vatutin

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arXiv · 1710.08724

Limit theorems for supercritical MBPRE with linear fractional offspring distributions

Wenming Hong·Minzhi Liu·Vladimir Vatutin

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Abstract

We investigate the limit behavior of supercritical multitype branching processes in random environments with linear fractional offspring distributions and show that there exists a phase transition in the behavior of local probabilites of the process affected by strongly and intermediately supercritical regimes. Some conditional limit theorems can also be obtained from the representation of generating functions.

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Wenming Hong, Minzhi Liu, Vladimir Vatutin. 2017-10-24. Limit theorems for supercritical MBPRE with linear fractional offspring distributions. https://arxiv.org/abs/1710.08724

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