Perturbation analysis of the extinction probability of a Markovian binary tree

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, which is a bound on the difference between the solutions of two nearby equations in terms of the perturbation magnitude. A posteriori error bound is also given, which is a bound on the distance between an approximate solution and the real solution, in terms of the residual of the approximate solution. Numerical experiments show that these bounds are fairly sharp.