38 citations · 121 across the 45 of their papers we have counts for
4 papers · 2 filters
Rosenthal-type inequalities for martingales in 2-smooth Banach spaces
Iosif Pinelis
Certain previously known upper bounds on the moments of the norm of martingales in 2-smooth Banach spaces are improved. Some of these improvements hold even for sums of independent…
Optimum bounds for the distributions of martingales in Banach spaces
Iosif Pinelis
A general device is proposed, which provides for extension of exponential inequalities for sums of independent real-valued random variables to those for martingales in the 2-smooth…
An exact bound on the truncated-tilted mean for symmetric distributions
Iosif Pinelis
An exact upper bound on the Winsorised-tilted mean of a symmetric random variable in terms of its second moment is given. Such results are used in work on nonuniform Berry--Esseen-…
On the supremum of the tails of normalized sums of independent Rademacher random variables
Iosif Pinelis
A well-known longstanding conjecture on the supremum of the tails of normalized sums of independent Rademacher random variables is disproved. A related conjecture, also recently di…