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

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
Creator
Contributor
Subject
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, 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"--
  • "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"--
Member of
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
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 227-234) 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 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
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
Publication
Bibliography note
Includes bibliographical references (p. 227-234) 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 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
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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