
Differentiability of Six Operators on Nonsmooth Functions and p-Variation
Springer (Publisher)
Published on 21. June 1999
Book
Paperback/Softback
X, 282 pages
978-3-540-65975-4 (ISBN)
Description
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.
More details
Series
Edition
1999 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
X, 282 p.
Dimensions
Height: 233 mm
Width: 155 mm
Thickness: 16 mm
Weight
443 gr
ISBN-13
978-3-540-65975-4 (9783540659754)
DOI
10.1007/BFb0100744
Schweitzer Classification
Persons
Content
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.