On Hoeffding's and Freedman's inequalities for supermartingale differences

Details On Hoeffding's and Freedman's inequalities for supermartingale differences On Hoeffding's and Freedman's inequalities for supermartingale differences

2011-09-20

arxiv.org/abs/1109.4359v3

Mathematics

Probability

24 pages

Scientific paper

We give an extension of the celebrated Hoeffding inequality to the case of
supermartingale differences bounded from above. In the case of independent
centered random variables we recover and improve the Hoeffding inequality. Our
inequalities also improve the well-known inequalities of Freedman, Bernstein,
Prohorov, Bennett and Nagaev.

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