Limit Theorems for Supercritical MBPRE with Linear Fractional Offspring Distributions
W. Hong, M. Liu, V.A. Vatutin
2019, v.25, Issue 1, 1-31
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.
Keywords: multitype branching process in random environments, supercritical, random walk, conditional limit theorem
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