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The Resource Normal approximations with Malliavin calculus : from Stein's method to universality, Ivan Nourdin, Giovanni Peccati
Normal approximations with Malliavin calculus : from Stein's method to universality, Ivan Nourdin, Giovanni Peccati
Resource Information
The item Normal approximations with Malliavin calculus : from Stein's method to universality, Ivan Nourdin, Giovanni Peccati represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Normal approximations with Malliavin calculus : from Stein's method to universality, Ivan Nourdin, Giovanni Peccati represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary

 "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, BreuerMajor theorems for fractional processes, recursive cumulant computations, optimal rates and universality results for homogeneous sums. Largely selfcontained, the book is perfect for selfstudy. 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"
 "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"
 Language
 eng
 Extent
 xiv, 239 pages
 Contents

 Malliavin operators in the onedimensional case
 Malliavin operators and isonormal Gaussian processes
 Stein's method for onedimensional normal approximations
 Multidimensional Stein's method
 Stein meets Malliavin : univariate normal approximations
 Multivariate normal approximations
 Exploring the BreuerMajor 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
 Isbn
 9781107017771
 Label
 Normal approximations with Malliavin calculus : from Stein's method to universality
 Title
 Normal approximations with Malliavin calculus
 Title remainder
 from Stein's method to universality
 Statement of responsibility
 Ivan Nourdin, Giovanni Peccati
 Language
 eng
 Summary

 "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, BreuerMajor theorems for fractional processes, recursive cumulant computations, optimal rates and universality results for homogeneous sums. Largely selfcontained, the book is perfect for selfstudy. 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"
 "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"
 Assigning source

 Provided by publisher
 Provided by publisher
 Cataloging source
 DLC
 http://library.link/vocab/creatorName
 Nourdin, Ivan
 Index
 index present
 LC call number
 QA221
 LC item number
 .N68 2012
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1975
 http://library.link/vocab/relatedWorkOrContributorName
 Peccati, Giovanni
 Series statement
 Cambridge tracts in mathematics
 Series volume
 192
 http://library.link/vocab/subjectName

 Approximation theory
 Malliavin calculus
 MATHEMATICS
 Approximation theory
 Malliavin calculus
 Label
 Normal approximations with Malliavin calculus : from Stein's method to universality, Ivan Nourdin, Giovanni Peccati
 Bibliography note
 Includes bibliographical references (p. 227234) and indexes
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Malliavin operators in the onedimensional case  Malliavin operators and isonormal Gaussian processes  Stein's method for onedimensional normal approximations  Multidimensional Stein's method  Stein meets Malliavin : univariate normal approximations  Multivariate normal approximations  Exploring the BreuerMajor 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
 Dimensions
 23 cm.
 Extent
 xiv, 239 pages
 Isbn
 9781107017771
 Isbn Type
 (hardback)
 Lccn
 2012010132
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 System control number

 (OCoLC)772971670
 (OCoLC)ocn772971670
 Label
 Normal approximations with Malliavin calculus : from Stein's method to universality, Ivan Nourdin, Giovanni Peccati
 Bibliography note
 Includes bibliographical references (p. 227234) and indexes
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Malliavin operators in the onedimensional case  Malliavin operators and isonormal Gaussian processes  Stein's method for onedimensional normal approximations  Multidimensional Stein's method  Stein meets Malliavin : univariate normal approximations  Multivariate normal approximations  Exploring the BreuerMajor 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
 Dimensions
 23 cm.
 Extent
 xiv, 239 pages
 Isbn
 9781107017771
 Isbn Type
 (hardback)
 Lccn
 2012010132
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 System control number

 (OCoLC)772971670
 (OCoLC)ocn772971670
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