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for questions involving inequalities, upper and lower bounds.

1 vote
1 answer
282 views

Exponential upper bounds for sums of martingale differences

I am interested in the exponential inequalities of the form \begin{equation} \label{eq:main_ineq} E[\exp(hS_{n})] \leq \exp(\frac{\Sigma^2}{M^2} (\exp(hM)-hM-1)) \end{equation} Such upper bound holds for … Equation 1 in herein book Concentration Inequalities', by Boucheron, Lugosi and Massart page 25-26. ). …
Oleksandr Z.'s user avatar
3 votes
1 answer
152 views

Question on example 3.0.1 in Yurinsky's book "Sums and Gaussian vectors"

Good day to All. Let $S_{1,n} = \sum_{i=1}^{n}\xi_{i}$, where $(\xi_{i})_{i \in \mathbb{N}}$ be independent RV with values in some Banach space. On pages 79-80 in this book author provides an examp …
Oleksandr Z.'s user avatar