An Order-Theoretic Mixing Condition for Monotone Markov Chains
We discuss stability of discrete-time Markov chains satisfying monotonicity and an order-theoretic mixing condition that can be seen as an alternative to irreducibility. A chain satisfying these conditions has at most one stationary distribution. Moreover, if there is a stationary distribution, then the chain is stable in an order-theoretic sense.
Markov chains; monotonicity; mixing; irreducibility; coupling
RIEB, Kobe University
Rokkodai-cho, Nada-ku, Kobe
Research School of Economics, Australian National University, Canberra, ACT, Australia