Perturbation analysis of the extinction probability of a Markovian binary tree

Abstract

The extinction probability of the Markovian Binary Tree (MBT) is the minimal nonnegative solution of a Quadratic Vector Equation (QVE). In this paper, we present a perturbation analysis for the extinction probability of a supercritical MBT. We derive a perturbation bound for the minimal nonnegative solution of the QVE, and an error bound is also given, which can be used to measure the quality of an approximation solution. Numerical tests show that these bounds are fairly sharp.