### Yale University

Department of Statistics

Seminar

#### Monday, May 6, 1996

Victor H. de la Pena

Department of Statistics

Columbia University

#### Decoupling Inequalities: A Second Generation of Martingale Inequalities

The theory of martingale inequalities has been central in the development of
modern probability theory. Recently this theory has been expanded widely
through the introduction of decoupling inequalities, which provide natural
extensions in cases where the variables take values in general spaces or when
a martingale structure is not available. Typically, decoupling inequalities
are used to transform problems involving sums of dependent random variables
into problems involving sums of (conditionally) independent random variables.
This transformation particularly permits the use of traditional results when
dealing with sums of dependent variables. In this paper an account of the
theory of decoupling inequalities is given with emphasis on its relations to
the theory of martingale inequalities, and its applications and extensions to
a wide range of problems, including best constants on martingale
inequalities, stopping time problems, U-statistics, random graphs, quadratic
forms and stochastic integration.

#### Seminar to be held in Room 107, 24 Hillhouse@ 4:15 pm