Stochastic Safety for Markov Chains
Manuela L. Bujorianu, Rafał Wiśniewski, Evangelos K. Boulougouris · IEEE Control Systems Letters · 2020
In this letter, we study the so-called p-safety of a Markov chain. We say that a state is p-safe in a state space S with respect to an unsafe set U if the process stays in the state space and hits the set U with the probability less than p. We show several ways of computing p-safety: by means the Dirichlet problem, the evolution equation, the barrier certificates, and the Martin kernel. The set of barrier certificates forms a cone. We show how to generate barrier certificates from the set of extreme points of a cone base.