عنوان

Normal approximations with Malliavin calculus :

شابک

1107017777 (hardback)

شابک

9781107017771 (hardback)

شماره

dltt

عنوان اصلي

Normal approximations with Malliavin calculus :

نام عام مواد

[Book]

ساير اطلاعات عنواني

from Stein's method to universality /

نام نخستين پديدآور

Ivan Nourdin, Giovanni Peccati

نام خاص و کميت اثر

xiv, 239 pages ;

ابعاد

23 cm

عنوان فروست

Cambridge tracts in mathematics ;

مشخصه جلد

192

متن يادداشت

Includes bibliographical references (pages 227-234) and indexes

متن يادداشت

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

بدون عنوان

0

متن يادداشت

"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"--

متن يادداشت

"This is a text about probabilistic approximations, which are mathematical statements providing estimates of the distance between the laws of two random objects. As the title suggests, we will be mainly interested in approximations involving one or more normal (equivalently called Gaussian) random elements. Normal approximations are naturally connected with central limit theorems (CLTs), i.e. convergence results displaying a Gaussian limit, and are one of the leading themes of the whole theory of probability"--

موضوع مستند نشده

Approximation theory

موضوع مستند نشده

Malliavin calculus

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Nourdin, Ivan

مستند نام اشخاص تاييد نشده

Peccati, Giovanni,1975-

تاريخ عمليات

20141128182522.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y