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Normal approximations with Malliavin...

Nourdin, Ivan.

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Normal approximations with Malliavin calculus = from Stein's method to universality /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Normal approximations with Malliavin calculus/ Ivan Nourdin, Giovanni Peccati.
其他題名:	from Stein's method to universality /
作者:	Nourdin, Ivan.
其他作者:	Peccati, Giovanni,
出版者:	Cambridge :Cambridge University Press, : 2012.,
面頁冊數:	xiv, 239 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	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.
標題:	Approximation theory. -
電子資源:	https://doi.org/10.1017/CBO9781139084659
ISBN:	9781139084659

Normal approximations with Malliavin calculus = from Stein's method to universality /
Nourdin, Ivan.

Normal approximations with Malliavin calculusfrom Stein's method to universality /[electronic resource] :Ivan Nourdin, Giovanni Peccati. - Cambridge :Cambridge University Press,2012. - xiv, 239 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;192. - Cambridge tracts in mathematics ;192..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

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.

ISBN: 9781139084659Subjects--Topical Terms:

628068
Approximation theory.

LC Class. No.: QA221 / .N68 2012

Dewey Class. No.: 519.23

Normal approximations with Malliavin calculus = from Stein's method to universality /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 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.
520 $a 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.
650 0 $a Approximation theory. $3 628068
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