Differentiability of Six Operators on Nonsmooth Functions and p-Variation / Edition 1

by R. M. Dudley, J. Qian, R. Norvaisa

Overview

The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.

Product Details

ISBN-13:	9783540659754
Publisher:	Springer Berlin Heidelberg
Publication date:	07/30/1999
Series:	Lecture Notes in Mathematics , #1703
Edition description:	1999
Pages:	282
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

A survey on differentiability of six operators in relation to probability and statistics.- Product integrals, young integrals and p-variation.- Differentiability of the composition and quantile operators for regulated and A. E. continuous functions.- Bibliographies on p-variation and—-variation.