Normal Approximations with Malliavin Calculus

Normal Approximations with Malliavin Calculus : From Stein's Method to Universality

4 (1 rating by Goodreads)
  • Electronic book text
By (author)  , By (author) 

List price: US$63.99

Currently unavailable

We can notify you when this item is back in stock

Add to wishlist

AbeBooks may have this title (opens in new window).

Try AbeBooks

Description

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.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 1139369075
  • 9781139369077

About Ivan Nourdin

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.show more

Table of contents

Preface; Introduction; 1. Malliavin operators in the one-dimensional case; 2. Malliavin operators and isonormal Gaussian processes; 3. Stein's method for one-dimensional normal approximations; 4. Multidimensional Stein's method; 5. Stein meets Malliavin: univariate normal approximations; 6. Multivariate normal approximations; 7. Exploring the Breuer-Major Theorem; 8. Computation of cumulants; 9. Exact asymptotics and optimal rates; 10. Density estimates; 11. Homogeneous sums and universality; Appendix 1. Gaussian elements, cumulants and Edgeworth expansions; Appendix 2. Hilbert space notation; Appendix 3. Distances between probability measures; Appendix 4. Fractional Brownian motion; Appendix 5. Some results from functional analysis; References; Index.show more

Review quote

'This monograph is a nice and excellent introduction to Malliavin calculus and its application to deducing quantitative central limit theorems in combination with Stein's method for normal approximation. It provides a self-contained and appealing presentation of the recent work developed by the authors, and it is well tailored for graduate students and researchers.' David Nualart, Mathematical Reviews 'The book contains many examples and exercises which help the reader understand and assimilate the material. Also bibliographical comments at the end of each chapter provide useful references for further reading.' Bulletin of the American Mathematical Societyshow more

Rating details

1 ratings
4 out of 5 stars
5 0% (0)
4 100% (1)
3 0% (0)
2 0% (0)
1 0% (0)
Book ratings by Goodreads
Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. Close X