Normal Approximations with Malliavin Calculus : From Stein's Method to Universality.

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Shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Nourdin, Ivan
Otros Autores: Peccati, Giovanni, 1975-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2012.
Colección:Cambridge Tracts in Mathematics, 192.
Temas:
Approximation theory.
Malliavin calculus.
Théorie de l'approximation.
Calcul de Malliavin.
MATHEMATICS > Probability & Statistics > General.
MATHEMATICS > Probability & Statistics > Stochastic Processes.
Aproximación, Teoría de
Approximation theory
Malliavin calculus
Acceso en línea:Texto completo

MARC

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100 1 |a Nourdin, Ivan. 
245 1 0 |a Normal Approximations with Malliavin Calculus :  |b From Stein's Method to Universality. 
260 |a Cambridge :  |b Cambridge University Press,  |c 2012. 
300 |a 1 online resource (256 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Cambridge Tracts in Mathematics, 192 ;  |v v. 192 
588 0 |a Print version record. 
505 0 |a Cover; CAMBRIDGE TRACTS IN MATHEMATICS: GENERAL EDITORS; Title; Copyright; Dedication; Contents; Preface; Introduction; 1 Malliavin operators in the one-dimensional case; 1.1 Derivative operators; 1.2 Divergences; 1.3 Ornstein-Uhlenbeck operators; 1.4 First application: Hermite polynomials; 1.5 Second application: variance expansions; 1.6 Third application: second-order Poincaré inequalities; 1.7 Exercises; 1.8 Bibliographic comments; 2 Malliavin operators and isonormal Gaussian processes; 2.1 Isonormal Gaussian processes; 2.2 Wiener chaos; 2.3 The derivative operator. 
505 8 |a 2.4 The Malliavin derivatives in Hilbert spaces2.5 The divergence operator; 2.6 Some Hilbert space valued divergences; 2.7 Multiple integrals; 2.8 The Ornstein-Uhlenbeck semigroup; 2.9 An integration by parts formula; 2.10 Absolute continuity of the laws of multiple integrals; 2.11 Exercises; 2.12 Bibliographic comments; 3 Stein's method for one-dimensional normal approximations; 3.1 Gaussian moments and Stein's lemma; 3.2 Stein's equations; 3.3 Stein's bounds for the total variation distance; 3.4 Stein's bounds for the Kolmogorov distance; 3.5 Stein's bounds for the Wasserstein distance. 
505 8 |a 3.6 A simple example3.7 The Berry-Esseen theorem; 3.8 Exercises; 3.9 Bibliographic comments; 4 Multidimensional Stein's method; 4.1 Multidimensional Stein's lemmas; 4.2 Stein's equations for identity matrices; 4.3 Stein's equations for general positive definite matrices; 4.4 Bounds on the Wasserstein distance; 4.5 Exercises; 4.6 Bibliographic comments; 5 Stein meets Malliavin: univariate normal approximations; 5.1 Bounds for general functionals; 5.2 Normal approximations on Wiener chaos; 5.2.1 Some preliminary considerations; 5.3 Normal approximations in the general case; 5.3.1 Main results. 
505 8 |a 5.4 Exercises5.5 Bibliographic comments; 6 Multivariate normal approximations; 6.1 Bounds for general vectors; 6.2 The case of Wiener chaos; 6.3 CLTs via chaos decompositions; 6.4 Exercises; 6.5 Bibliographic comments; 7 Exploring the Breuer-Major theorem; 7.1 Motivation; 7.2 A general statement; 7.3 Quadratic case; 7.4 The increments of a fractional Brownian motion; 7.5 Exercises; 7.6 Bibliographic comments; 8 Computation of cumulants; 8.1 Decomposing multi-indices; 8.2 General formulae; 8.3 Application to multiple integrals; 8.4 Formulae in dimension one; 8.5 Exercises. 
505 8 |a 8.6 Bibliographic comments9 Exact asymptotics and optimal rates; 9.1 Some technical computations; 9.2 A general result; 9.3 Connections with Edgeworth expansions; 9.4 Double integrals; 9.5 Further examples; 9.6 Exercises; 9.7 Bibliographic comments; 10 Density estimates; 10.1 General results; 10.2 Explicit computations; 10.3 An example; 10.4 Exercises; 10.5 Bibliographic comments; 11 Homogeneous sums and universality; 11.1 The Lindeberg method; 11.2 Homogeneous sums and influence functions; 11.3 The universality result; 11.4 Some technical estimates; 11.5 Proof of Theorem 11.3.1. 
500 |a 11.6 Exercises. 
520 |a Shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus. 
504 |a Includes bibliographical references and index. 
590 |a eBooks on EBSCOhost  |b EBSCO eBook Subscription Academic Collection - Worldwide 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Approximation theory. 
650 0 |a Malliavin calculus. 
650 6 |a Théorie de l'approximation. 
650 6 |a Calcul de Malliavin. 
650 7 |a MATHEMATICS  |x Probability & Statistics  |x General.  |2 bisacsh 
650 7 |a MATHEMATICS  |x Probability & Statistics  |x Stochastic Processes.  |2 bisacsh 
650 0 7 |a Aproximación, Teoría de  |2 embucm 
650 7 |a Approximation theory  |2 fast 
650 7 |a Malliavin calculus  |2 fast 
700 1 |a Peccati, Giovanni,  |d 1975-  |1 https://id.oclc.org/worldcat/entity/E39PCjHW3xR6VdxggCgh4BRBT3 
758 |i has work:  |a Normal approximations with Malliavin calculus (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCG3RkMDtRqjXjvR8WFHq6X  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version:  |a Nourdin, Ivan.  |t Normal Approximations with Malliavin Calculus : From Stein's Method to Universality.  |d Cambridge : Cambridge University Press, ©2012  |z 9781107017771 
830 0 |a Cambridge Tracts in Mathematics, 192. 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=880643  |z Texto completo 
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