Normal Approximations with Malliavin Calculus (Hardcover)

Ivan Nourdin

ISBN 10: 1107017777 / ISBN 13: 9781107017771

Editore: Cambridge University Press, Cambridge, 2012

Hardcover. 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 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 book studies normal approximations by means of two powerful probabilistic techniques: the Malliavin calculus and Stein's method. Largely self-contained it is perfect for self-study and will appeal both to researchers and to graduate students in probability and statistics. This item is printed on demand. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Codice articolo 9781107017771

Riassunto:

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

Informazioni sugli autori: 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.

Dati bibliografici

Titolo: Normal Approximations with Malliavin ...
Casa editrice: Cambridge University Press, Cambridge
Data di pubblicazione: 2012
Legatura: Hardcover
Condizione: new