On Azuma-Type Inequalities for Banach Space-Valued Martingales
نویسندگان
چکیده
In this paper, we will study concentration inequalities for Banach space-valued martingales. Firstly, prove that a space X is linearly isomorphic to p-uniformly smooth ( $$1<p\le 2$$ ) if and only an Azuma-type inequality holds X-valued This can be viewed as generalization of Pinelis’ work on Azuma martingales with values in 2-uniformly spaces. Secondly, self-normalized sums presented. Finally, some further martingales, such moment double indexed dyadic De la Peña-type conditionally symmetric also discussed.
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ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2021
ISSN: ['1572-9230', '0894-9840']
DOI: https://doi.org/10.1007/s10959-021-01086-5