Overview
- A self-contained and probability-oriented introduction to the theory of lattice of partitions, with a unique software implementation that makes our book an ideal introduction to the field
- A complete and self-contained combinatorial analysis of cumulants and diagram formulae, unique in its genre
- An introduction to Wiener chaos, and a new combinatorial interpretation of recently proved limit theorems
- Includes supplementary material: sn.pub/extras
Part of the book series: Bocconi & Springer Series (BS, volume 1)
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Table of contents (12 chapters)
Keywords
About this book
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.” (Gábor Szűcs, Acta Scientiarum Mathematicarum (Szeged), Vol. 77 (3-4), 2011)
Authors and Affiliations
About the authors
Bibliographic Information
Book Title: Wiener Chaos: Moments, Cumulants and Diagrams
Book Subtitle: A survey with Computer Implementation
Authors: Giovanni Peccati, Murad S. Taqqu
Series Title: Bocconi & Springer Series
DOI: https://doi.org/10.1007/978-88-470-1679-8
Publisher: Springer Milano
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Milan 2011
Hardcover ISBN: 978-88-470-1678-1Published: 28 December 2010
Softcover ISBN: 978-88-470-5604-6Published: 12 October 2014
eBook ISBN: 978-88-470-1679-8Published: 06 April 2011
Series ISSN: 2039-1471
Series E-ISSN: 2039-148X
Edition Number: 1
Number of Pages: XIII, 274
Topics: Probability Theory and Stochastic Processes, Quantitative Finance, Combinatorics, Measure and Integration