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Approximating kth-order two-state Markov chains
Published online by Cambridge University Press: 14 July 2016
Abstract
In this paper, we consider kth-order two-state Markov chains {Xi} with stationary transition probabilities. For k = 1, we construct in detail an upper bound for the total variation d(Sn, Y) = Σx |𝐏(Sn = x) − 𝐏(Y = x)|, where Sn = X1 + · ··+ Xn and Y is a compound Poisson random variable. We also show that, under certain conditions, d(Sn, Y) converges to 0 as n tends to ∞. For k = 2, the corresponding results are given without derivation. For general k ≧ 3, a conjecture is proposed.
Keywords
MSC classification
Secondary:
60F05: Central limit and other weak theorems
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- Research Papers
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- Copyright © Applied Probability Trust 1992
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