Positive dependence in Markov chains

A general notion of positive dependence among successive observations in a finite-state stationary process is studied, with particular attention to the case of a stationary ergodic Markov chain. This dependence condition can be expressed as a positivity condition on the joint probability matrices of pairs of observations. Some useful conditions equivalent to positive dependence are obtained for reversible chains, but shown not to be equivalent for nonreversible chains.