Overview
The concept of Wiener chaos generalizes to an infinite-dimensional setting the properties of orthogonal polynomials associated with probability distributions on the real line. It plays a crucial role in modern probability theory, with applications ranging from Malliavin calculus to stochastic differential equations and from probabilistic approximations to mathematical finance. This book is concerned with combinatorial structures arising from the study of chaotic random variables related to infinitely divisible random measures. The combinatorial structures involved are those of partitions of finite sets, over which Möbius functions and related inversion formulae are defined. This combinatorial standpoint (which is originally due to Rota and Wallstrom) provides an ideal framework for diagrams, which are graphical devices used to compute moments and cumulants of random variables. Several applications are described, in particular, recent limit theorems for chaotic random variables. An Appendix presents a computer implementation in MATHEMATICA for many of the formulae.
Full Product Details
Author: Giovanni Peccati ,
Murad S. Taqqu
Publisher: Springer Verlag
Imprint: Springer Verlag
Edition: 2011 ed.
Volume: 1
Dimensions:
Width: 15.50cm
, Height: 1.50cm
, Length: 23.50cm
Weight: 0.454kg
ISBN: 9788847056046
ISBN 10: 8847056047
Pages: 274
Publication Date: 12 October 2014
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
From the book reviews: The objective of this book is to provide a detailed account of the combinatorial structures arising from the study of multiple stochastic integrals. ... the presentation is very clear, with all the necessary proofs and examples. The authors clearly accomplish the three goals they list in the introduction (to provide a unified approach to the diagram method using set partition, to give a combinatorial analysis of multiple stochastic integrals in the most general setting, and to discuss chaotic limit theorems). (Sergey V. Lototsky, Mathematical Reviews, Issue 2012 d) The book provides a comprehensive and detailed introduction to the theory of multiple stochastic integrals and some results for the Wiener chaos representation of random variables. ... The book is recommended for anyone who needs a precise guidance to the theory. (Gabor Szucs, Acta Scientiarum Mathematicarum (Szeged), Vol. 77 (3-4), 2011)
From the book reviews: “The objective of this book is to provide a detailed account of the combinatorial structures arising from the study of multiple stochastic integrals. … the presentation is very clear, with all the necessary proofs and examples. The authors clearly accomplish the three goals they list in the introduction (to provide a unified approach to the diagram method using set partition, to give a combinatorial analysis of multiple stochastic integrals in the most general setting, and to discuss chaotic limit theorems).” (Sergey V. Lototsky, Mathematical Reviews, Issue 2012 d) “The book provides a comprehensive and detailed introduction to the theory of multiple stochastic integrals and some results for the Wiener chaos representation of random variables. … The book is recommended for anyone who needs a precise guidance to the theory.” (Gábor Szűcs, Acta Scientiarum Mathematicarum (Szeged), Vol. 77 (3-4), 2011)
From the book reviews: The objective of this book is to provide a detailed account of the combinatorial structures arising from the study of multiple stochastic integrals. ... the presentation is very clear, with all the necessary proofs and examples. The authors clearly accomplish the three goals they list in the introduction (to provide a unified approach to the diagram method using set partition, to give a combinatorial analysis of multiple stochastic integrals in the most general setting, and to discuss chaotic limit theorems). (Sergey V. Lototsky, Mathematical Reviews, Issue 2012 d) The book provides a comprehensive and detailed introduction to the theory of multiple stochastic integrals and some results for the Wiener chaos representation of random variables. ... The book is recommended for anyone who needs a precise guidance to the theory. (Gabor Szucs, Acta Scientiarum Mathematicarum (Szeged), Vol. 77 (3-4), 2011)
From the book reviews: The objective of this book is to provide a detailed account of the combinatorial structures arising from the study of multiple stochastic integrals. ... the presentation is very clear, with all the necessary proofs and examples. The authors clearly accomplish the three goals they list in the introduction (to provide a unified approach to the diagram method using set partition, to give a combinatorial analysis of multiple stochastic integrals in the most general setting, and to discuss chaotic limit theorems). (Sergey V. Lototsky, Mathematical Reviews, Issue 2012 d) The book provides a comprehensive and detailed introduction to the theory of multiple stochastic integrals and some results for the Wiener chaos representation of random variables. ... The book is recommended for anyone who needs a precise guidance to the theory. (Gabor Szucs, Acta Scientiarum Mathematicarum (Szeged), Vol. 77 (3-4), 2011)
Author Information
Giovanni Peccati is a Professor of Stochastic Analysis and Mathematical Finance at Luxembourg University. Murad S. Taqqu is a Professor of Mathematics and Statistics at Boston University.
