Martingale Versions of Yano’s Extrapolation Inequalities

Concentration inequalities and martingale inequalities — a survey

We examine a number of generalized and extended versions of concentration inequalities and martingale inequalities. These inequalities are effective for analyzing processes with quite general conditions as illustrated in an example for an infinite Polya process and webgraphs.

On the Range Space of Yano’s Extrapolation Theorem and New Extrapolation Estimates at Infinity

A Trajectorial Interpretation of Doob’s Martingale Inequalities

We present a unified approach to Doob’s Lp maximal inequalities for 1 ≤ p < ∞. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a natural interpretation in terms of robust hedging. Moreover our deterministic inequalities lead to new versions of Doob’s maximal inequalities. These are best possib...

Extrapolation of Weighted Norm Inequalities for Multivariable Operators and Applications

Two versions of Rubio de Francia’s extrapolation theorem for multivariable operators of functions are obtained. One version assumes an initial estimate with different weights in each space and implies boundedness on all products of Lebesgue spaces. Another version assumes an initial estimate with the same weight but yields boundedness on a product of Lebesgue spaces whose indices lie on a line....

Concentration Inequalities for Dependent Random Variables via the Martingale Method

Abstract: We use the martingale method to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, we obtain bounds on certain martingale differences associated with the random sequences, which may be of independent interest. As an applicatio...