Differentiability of Six Operators on Nonsmooth Functions and P-Variation

ISBN-10: 3540659757
ISBN-13: 9783540659754
Category: Mathematics / Mathematical Analysis
Pages: 277
Language: English
Published: 1999-06-21
Publisher: Springer Science & Business
Authors: R. M. Dudley, R. Norvaiša

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.

Get the book

Other editions

Differentiability of Six Operators on Nonsmooth Functions and p-Variation
- 2006-12-08
- 289 pages
- Ebook
- Springer

Similar books

Differentiability of Six Operators on Nonsmooth Functions and P-Variation
By R. M. Dudley, R. Norvai a
Differentiability of Six Operators on Nonsmooth Functions and P-Variation
Selected Works of R.M. Dudley
By R. Norvaiša, Evarist Giné, Vladimir Koltchinskii
... differentiability, p-variation and uniform Donsker classes. Ann ... operators for p-variation norms. Ann. Statist., 22:1–20, 1994 ...
Concrete Functional Calculus
By R. M. Dudley, R. Norvaiša
This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability.
$C^\infinity - Differentiable Spaces$

C^\infinity - Differentiable Spaces
By Juan A. Navarro González, Juan B. Sancho de Salas
... P. Bernard . IX , 291 pages . 1999 . Vol . 1718 : A. Eberle , Uniqueness and Non - Uniqueness of Semigroups Generated by Singular ...
Regular Variation and Differential Equations
By Vojislav Maric
... Operators and Hardy's Inequality . IX , 114 pages . 1998 . Vol ... P. Pragacz , Schubert Varieties and Degeneracy Loci . XI , 148 ...
Topology of Singular Fibers of Differentiable Maps
By Osamu Saeki
... P. Pragacz, Schubert Varieties and Degeneracy Loci, XI, 148 pages ... Operators and Stochastic Flows. IV, 118 pages. 1999. Vol. 1721 ...
Brownian Motion: A Guide to Random Processes and Stochastic Calculus
By René L. Schilling
... p - variation of stochastic processes is quite difficult , and ... functions of the Gaussian process . [ 64 ] Dudley , Norvaiša : An ...
Stable Approximate Evaluation of Unbounded Operators
By C. W. Groetsch
Ecole d' Eté de Probabilités de Saint-Flour XXIX-1999. Editor: P. Bernard (2002) Vol. 1782: C.-H. Chu, ... 1801: J. Azéma, M. Émery, M. Ledoux, M. Yor (Eds.), Séminaire de Probabilités XXXVI (2003) Vol. 1802: V. Capasso, E. Merzbach, ...
Stochastic Calculus of Variations: For Jump Processes
By Yasushi Ishikawa
... Differentiability of six operators on nonsmooth functions and p - variation . Lecture Notes in Mathematics 1703. Berlin , Germany ...
Big Queues
By Damon J. Wischik, Ayalvadi J. Ganesh, Neil O'Connell
... Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators. VIII, 262 pages. 1999. Vol. 1719: K. R. Meyer, Periodic ...