Normal approximations with Malliavin calculus : from Stein's method to universality / / Ivan Nourdin, Giovanni Peccati [[electronic resource]]

• Autore: Nourdin Ivan
• Pubblicazione: Cambridge : , : Cambridge University Press, , 2012
• Descrizione fisica: 1 online resource (xiv, 239 pages) : digital, PDF file(s)
• Disciplina: 519.2/3
• Soggetto topico: Approximation theory; Malliavin calculus
• Classificazione: MAT029000
• Persona (resp. second.): PeccatiGiovanni <1975->
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Malliavin operators in the one-dimensional case -- Malliavin operators and isonormal Gaussian processes -- Stein's method for one-dimensional normal approximations -- Multidimensional Stein's method -- Stein meets Malliavin : univariate normal approximations -- Multivariate normal approximations -- Exploring the Breuer-Major theorem -- Computation of cumulants -- Exact asymptotics and optimal rates -- Density estimates -- Homogeneous sums and universality -- Gaussian elements, cumulants and Edgeworth expansions -- Hilbert space notation -- Distances between probability measures -- Fractional Brownian motion -- Some results from functional analysis.
• Sommario/riassunto: Stein's method is a collection of probabilistic techniques that allow one to assess the distance between two probability distributions by means of differential operators. In 2007, the authors discovered that one can combine Stein's method with the powerful Malliavin calculus of variations, in order to deduce quantitative central limit theorems involving functionals of general Gaussian fields. This book provides an ideal introduction both to Stein's method and Malliavin calculus, from the standpoint of normal approximations on a Gaussian space. Many recent developments and applications are studied in detail, for instance: fourth moment theorems on the Wiener chaos, density estimates, Breuer-Major theorems for fractional processes, recursive cumulant computations, optimal rates and universality results for homogeneous sums. Largely self-contained, the book is perfect for self-study. It will appeal to researchers and graduate students in probability and statistics, especially those who wish to understand the connections between Stein's method and Malliavin calculus.
• Titolo autorizzato: Normal approximations with Malliavin calculus
• ISBN: 1-107-23077-2; 1-280-87800-2; 1-139-37878-3; 9786613719317; 1-139-37592-X; 1-139-08465-8; 1-139-38021-4; 1-139-37193-2; 1-139-37735-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910818152303321
• Lo trovi qui: Univ. Federico II
• Serie: Cambridge tracts in mathematics ; ; 192.