Convergence of series of conditional expectations

M. Peligrad and C. Peligrad

Statistics & Probability Letters, 2023, vol. 200, issue C

Abstract: This paper deals with almost sure convergence 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 of moments of individual summands.

Keywords: Almost sure convergence; Markov chains; Nonstationary sequences; Maximal inequalities; Smooth Banach spaces (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2023.109869

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