Multi-type branching in varying environments
John D. Biggins
Prob and Stat Section, Univ of Sheffield, United Kingdom
Abstract
In this talk I will examine issues connected with the convergence of
the suitably normalised numbers in a multi-type Galton-Watson process
in a varying environment. The product of the offspring mean matrices
describes the growth in mean of the process; a good description of
such products is obtained through their positive harmonic functions.
Informally, these harmonic functions catch different possible
asymptotic behaviour in the products, and hence in the process. In the
simplest case (ie the homogenous, irreducible one) there is only one
harmonic function and so only one limiting behaviour (ie just one W).
