EXISTENCE OF A TRIAL FUNCTION FOR ESTIMATING THE MOMENTS OF THE STATIONARY DISTRIBUTION OF A MARKOV CHAIN.

The paper is logically allied to a recent paper by the authors which proposed a method of estimating the moments of the stationary distribution of a Markov chain by the method of trial functions. A question arose regarding the generality of this method, namely the extent to which the condition of existence of a trial function W with specified properties for estimating the stationary mean integral Vd pi of the (moment) function V is a restrictive one. Here it is shown that, under natural assumptions, there exists a trial function that is finite pi -almost everywhere. In this respect, therefore, the proposed method is universal.