Convergence of series of conditional expectations
Copyright policy )Convergence of series of conditional expectations
This paper deals with rates of convergence in the strong law of large numbers, in the Baum-Katz form, for partial sums of Banach space valued random variables. The results are then applied to solve similar problems for weighted partial sums of conditional expectations. They are further used to treat partial sums of powers of a reversible Markov chain operator. The method of proof is based on martingale approximation. The conditions are expressed in terms moments of the individual summands.
11 pages
- University of Cincinnati United States
- University of Cincinnati Main Campus United States
- University System of Ohio United States
Strong limit theorems, maximal inequalities, Markov chains, Probability (math.PR), Markov chains (discrete-time Markov processes on discrete state spaces), nonstationary sequences, FOS: Mathematics, Inequalities; stochastic orderings, smooth Banach spaces, Probabilistic methods in Banach space theory, almost sure convergence, Mathematics - Probability
Strong limit theorems, maximal inequalities, Markov chains, Probability (math.PR), Markov chains (discrete-time Markov processes on discrete state spaces), nonstationary sequences, FOS: Mathematics, Inequalities; stochastic orderings, smooth Banach spaces, Probabilistic methods in Banach space theory, almost sure convergence, Mathematics - Probability
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