A Polynomial Time Algorithm for Computing Extinction Probabilities of Multitype Branching Processes

A Polynomial Time Algorithm for Computing Extinction Probabilities of Multitype Branching Processes

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/ ), where > 0 is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We use this result to resolve several open ...

Explorer A polynomial time algorithm for computing extinction probabilities of multi - type branching processes

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/ ), where > 0 is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We use this result to resolve several open ...

Extinction times in Multitype Markov Branching Processes

In this paper, a distributional approximation to the time to extinction in a subcritical continuous-time Markov branching process is derived. A limit theorem for this distribution is established and the error in the approximation is quantified. The accuracy of the approximation is illustrated in an epidemiological example. Since Markov branching processes serve as approximations to nonlinear ep...

Limiting Distributions for Critical Multitype Branching Processes with Discrete Time(')

Relative frequencies in multitype branching processes

This paper considers the relative frequencies of distinct types of individuals in multitype branching processes. We prove that the frequencies are asymptotically multivariate normal when the initial number of ancestors is large and the time of observation is fixed. The result is valid for any branching process with a finite number of types; the only assumption required is that of independent in...