Precise Asymptotics in the Law of the Iterated Logarithm under Dependence

Abstract:Let {X n ; n ≥ 1} be a strictly stationary negatively associated sequence which satis- In this paper, we prove that, for b > −1, The result of Gut and Spǎtaru [2] is a special case of ours

Strong Law of Large Numbers for Countable Markov Chains Indexed by an Infinite Tree with Uniformly Bounded Degree

We study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for countable Markov chains indexed by an infinite tree with uniformly bounded degree, which extends the corresponding results of countable Markov chains indexed by a Cayley tree and generalizes the relative results of finite Markov chains indexed by a uniformly bounded tree