Normal Approximations with Malliavin Calculus: From Stein's Method to Universality: 192 (Cambridge Tracts in Mathematics, Series Number 192)

Ivan Nourdin, Giovanni Peccati

ISBN 10: 1107017777 / ISBN 13: 9781107017771

Published by Cambridge University Press 2012-05-10, 2012

About this Item

Seller Inventory # 6666-GRD-9781107017771

Bibliographic Details

• Title: Normal Approximations with Malliavin Calculus: From Stein's Method to Universality: 192 (Cambridge Tracts in Mathematics, Series Number 192)
• Publisher: Cambridge University Press 2012-05-10
• Publication Date: 2012
• Language: English
• ISBN 10: 1107017777
• ISBN 13: 9781107017771
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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.

About the Authors

Ivan Nourdin is Full Professor at Nancy University 1, France.

Giovanni Peccati is Full Professor in Stochastic Analysis and Finance at the University of Luxembourg.