Cantitate/Preț
Produs

Normal Approximations with Malliavin Calculus: From Stein's Method to Universality: Cambridge Tracts in Mathematics, cartea 192

Autor Ivan Nourdin, Giovanni Peccati
en Limba Engleză Hardback – 9 mai 2012
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.
Citește tot Restrânge

Din seria Cambridge Tracts in Mathematics

Preț: 55352 lei

Preț vechi: 62193 lei
-11% Nou

Puncte Express: 830

Preț estimativ în valută:
10594 11012$ 8776£

Carte tipărită la comandă

Livrare economică 05-19 februarie 25

Preluare comenzi: 021 569.72.76

Specificații

ISBN-13: 9781107017771
ISBN-10: 1107017777
Pagini: 254
Ilustrații: 70 exercises
Dimensiuni: 152 x 229 x 18 mm
Greutate: 0.5 kg
Ediția:New.
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Tracts in Mathematics

Locul publicării:New York, United States

Cuprins

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.

Recenzii

'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 Society

Notă biografică


Descriere

This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.