Differentiability of Six Operators on Nonsmooth Functions and p-Variation
Dudley, Richard M.
Differentiability of Six Operators on Nonsmooth Functions and p-Variation [electronic resource] / by Richard M. Dudley, Rimas NorvaiĊĦa. - X, 282 p. online resource. - Lecture Notes in Mathematics, 1703 0075-8434 ; . - Lecture Notes in Mathematics, 1703 .
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.
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.
9783540488149
10.1007/BFb0100744 doi
Operator theory.
Global analysis.
Mathematics.
Operator Theory.
Global Analysis and Analysis on Manifolds.
Real Functions.
QA329-329.9
515.724
Differentiability of Six Operators on Nonsmooth Functions and p-Variation [electronic resource] / by Richard M. Dudley, Rimas NorvaiĊĦa. - X, 282 p. online resource. - Lecture Notes in Mathematics, 1703 0075-8434 ; . - Lecture Notes in Mathematics, 1703 .
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.
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.
9783540488149
10.1007/BFb0100744 doi
Operator theory.
Global analysis.
Mathematics.
Operator Theory.
Global Analysis and Analysis on Manifolds.
Real Functions.
QA329-329.9
515.724