Strong Stationary Duality and Algebraic Duality for Continuous Time Möbius Monotone Markov Chains

Abstract

Under the assumption of Möbius monotonicity, we develop the theory of strong stationary duality for continuous time Markov chains on the finite partially ordered state space, we also construct a nonexplosive algebraic duality for continuous time Markov chains on Finally, we present an application to the two-dimensional birth and death chain.