Abstract:Abstract.For a Markov chain with an arbitrary nonempty state space, with stationary finitely additive transition probabilities and with initial distribution concentrated on a recurrent state, it is shown that the probability of every tail set is either zero or one. This generalizes and in particular gives an alternative proof of the result due to Blackwell and Freedman [1] in case the state space is countable and all transition probabilities are countably additive.
Abstract.A finitely additive generalization of Birkhoff s ergodic theorem is obtained which yields, in particular, strong laws of large numbers in the i.i.d. setting as well as for positive recurrent Markov chains.
Abstract.A finitely additive generalization of Birkhoff s ergodic theorem is obtained which yields, in particular, strong laws of large numbers in the i.i.d. setting as well as for positive recurrent Markov chains.
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