ABSTRACT
For describing "convergence to a long run steady state", perhaps the most widely used results identify conditions under which there is some time invariant probability measure rr such that, no matter what the initial X0 is, Xn converges in distribution to rr. That is, the n-step transition probability p(n) (x, dy), starting from an initial state x, converges weakly to a probability measure rr, irrespective of x. The class of processes for which we study such convergence corresponds to monotone nondecreasing an on an interval, or on appropriate subsets S c ll\l!k. Excepting for Sec. 7, where examples of multidimensional S are considered, the present chapter emphasizes the case of an interval.
