Lecture Notes in Mathematics

Differentiability of Six Operators on Nonsmooth Functions and p-Variation

Authors: Dudley, R. M., Norvaiša, R.

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About this book

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.

Table of contents (4 chapters)

  • A survey on differentiability of six operators in relation to probability and statistics

    Dudley, R. M. (et al.)

    Pages 1-72

  • Product integrals, young integrals and p-variation

    Dudley, R. M. (et al.)

    Pages 73-208

  • Differentiability of the composition and quantile operators for regulated and A. E. continuous functions

    Dudley, R. M. (et al.)

    Pages 209-240

  • Bibliographies on p-variation and ϕ-variation

    Dudley, R. M. (et al.)

    Pages 241-272

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-540-48814-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $52.00
price for USA
  • ISBN 978-3-540-65975-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Differentiability of Six Operators on Nonsmooth Functions and p-Variation
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1703
Copyright
1999
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-48814-9
DOI
10.1007/BFb0100744
Softcover ISBN
978-3-540-65975-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 282
Topics