We examine a number of generalized and extended versions of concentration inequalities
and martingale inequalities. These inequalities are effective for analyzing processes with …

We prove concentration inequalities for some classes of Markov chains and $\Phi $-mixing
processes, with constants independent of the size of the sample, that extend the inequalities …

We propose some explicit values for the constants involved in the exponential concentration
inequalities for empirical processes which are due to Talagrand. It has been shown by …

The paper is devoted to establishing some general exponential inequalities for
supermartingales. The inequalities improve or generalize many exponential inequalities of …

This chapter is devoted to concentration inequalities for martingales such as Azuma-
Hoeffding, Freedman, and De la Pena inequalities. Several extensions will also be provided …

We introduce new concentration inequalities for functions on product spaces. They allow to
obtain a Bennett type deviation bound for suprema of empirical processes indexed by upper …

The martingale method is used to establish concentration inequalities for a class of
dependent random sequences on a countable state space, with the constants in the …

We obtain exponential concentration inequalities for sub-additive functions of independent
random variables under weak conditions on the increments of those functions, like the …

We investigate a new methodology, worked out by Ledoux and Massart, to prove
concentration-of-measure inequalities. The method is based on certain modified logarithmic …

Concentration inequalities have been the subject of exciting developments during the last
two decades, and have been intensively studied and used as a powerful tool in various …