We devise a Monte Carlo based method for detecting whether a non-negative Markov chain is stable for a given set of potential parameterizations. More precisely, for a given set in parameter space, we develop an algorithm that is capable of deciding whether the set has a subset of positive Lebesgue measure for which the Markov chain is unstable. The approach is based on a variant of simulated annealing, and consequently only mild assumptions are needed to obtain performance guarantees.
I will illustrate the usage of our algorithm on models of communication networks.
This is joint work with Michel Mandjes (University of Amsterdam) and Neil Walton (The University of Manchester).