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- W3147320116 abstract "In this paper, we will study concentration inequalities for Banach space-valued martingales. Firstly, we prove that a Banach space X is linearly isomorphic to a p-uniformly smooth space ( $$1<ple 2$$ ) if and only if an Azuma-type inequality holds for X-valued martingales. This can be viewed as a generalization of Pinelis’ work on an Azuma inequality for martingales with values in 2-uniformly smooth spaces. Secondly, an Azuma-type inequality for self-normalized sums will be presented. Finally, some further inequalities for Banach space-valued martingales, such as moment inequalities for double indexed dyadic martingales and De la Peña-type inequalities for conditionally symmetric martingales, will also be discussed." @default.
- W3147320116 created "2021-04-13" @default.
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- W3147320116 date "2021-03-31" @default.
- W3147320116 modified "2023-10-18" @default.
- W3147320116 title "On Azuma-Type Inequalities for Banach Space-Valued Martingales" @default.
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- W3147320116 doi "https://doi.org/10.1007/s10959-021-01086-5" @default.
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