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Abstract:
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Consider a finite state, non-stationary Markov chain with transition kernels {P_n}, where P_n monotonically converges to P in a pointwise fashion. It has long been known that the limiting distribution of X_n, the location statistic of the chain at time n, exists. However, the question remains as to how one may easily determine whether y is asymptotically accessible from x, when we begin our chain in state x at a very distant point of the future. We present results appertaining to the limiting distribution, and an algorithm for determining when lim_m lim_n P^{m,m+n}(x,y)>0, indeed, what P^{m,m+n}(x,y)'s actual value is.
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