Convergence of vector-valued martingales with multidimensional indices
Copyright policy )Convergence of vector-valued martingales with multidimensional indices
This paper deals with almost sure convergence of Banach space valued martingales with d-dimensional indices. Generalizations of the reversed martingale convergence theorem and Cairoli's theorem on martingales of the class L(log L)\({}^{d-1}\) in spaces with RNP are presented. A multidimensional strong law of large numbers for vector-valued independent identically distributed random variables is also obtained.
multidimensional indices, Generalizations of martingales, Probability theory on linear topological spaces, Banach space valued martingales, almost sure convergence, Radon-Nikodým, Kreĭn-Milman and related properties
multidimensional indices, Generalizations of martingales, Probability theory on linear topological spaces, Banach space valued martingales, almost sure convergence, Radon-Nikodým, Kreĭn-Milman and related properties
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