A Perron vector iteration for QVEs

Abstract

Equation (1), with the additional conditions

$$M = I, a + b\left( {e,e} \right) = e$$

(3.1.1)

(i.e., the vector e is a solution, though not necessarily the minimal one), arises from the study of a class of branching processes known as Markovian binary trees. These processes model a population composed of a number of individuals, each of which may be in a state φ ∈ {1,2, ..., n}. The individuals evolve independently and have state-dependent probabilities of reproducing or dying. Here reproducing means that an individual in state i splits into two individuals in state j and k respectively; the probability of this event is represented by the term b_ijk in the equation, while the probability of an individual in state i dying is a _i .