Convergence of series of conditional expectations

Magda Peligrad; Costel Peligrad

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arXiv · 2212.01527

Convergence of series of conditional expectations

Magda Peligrad·Costel Peligrad

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Abstract

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.

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BibTeX RIS

Magda Peligrad, Costel Peligrad. 2022-12-23. Convergence of series of conditional expectations. https://arxiv.org/abs/2212.01527

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