1.

Record Nr.

UNINA9910462049403321

Autore

Nourdin Ivan

Titolo

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

Pubbl/distr/stampa

Cambridge : , : Cambridge University Press, , 2012

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

Descrizione fisica

1 online resource (xiv, 239 pages) : digital, PDF file(s)

Collana

Cambridge tracts in mathematics ; ; 192

Disciplina

519.2/3

Soggetti

Approximation theory

Malliavin calculus

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

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.

2.

Record Nr.

UNINA9910894720903321

Titolo

Abstracts of the proceedings of the Delaware Valley Ornithological Club of Philadelphia

Pubbl/distr/stampa

Philadelphia, Pa., 1890-1901

Descrizione fisica

Online-Ressource

Classificazione

BIODIV

Disciplina

590

Soggetti

Zeitschrift

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Periodico