Abstract
Let {X k ,J k } be a bivariate sequence of random variables, where J k is a finite ergodic Markov chain. Assume the random variables X k are conditionally independent given {Jk}. By decomposing \( {{S}_{n}} = \sum\nolimits_{{k = 1}}^{n} {{{X}_{k}}} \) the sum of i.i.d. random variables plus two ‘remainder’ terms, it is proved that Sn satisfies both the Strong Law of Large Numbers and the Law of the Iterated Logarithm under the conditions of finite first and second moments, respectively, of [Xk|Jk-1, Jk]
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