Wiener Chaos: Moments, Cumulants and Diagrams

A survey with Computer Implementation
2011
ISBN: 978-88-470-5604-6
Verlag: Springer Milan

Buch, Englisch, Band 1, 274 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 446 g

Reihe: Bocconi & Springer Series

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Taqqu, Murad S.

Peccati, Giovanni

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Finanz- und Versicherungsmathematik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Über Autor(innen)

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.