Giovanni Peccati

(Author)

Wiener Chaos: Moments, Cumulants and Diagrams: A Survey with Computer ImplementationHardcover, 28 December 2010

Wiener Chaos: Moments, Cumulants and Diagrams: A Survey with Computer Implementation
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Part of Series
Bocconi & Springer
Print Length
274 pages
Language
English
Publisher
Springer
Date Published
28 Dec 2010
ISBN-10
8847016789
ISBN-13
9788847016781

Description

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.

Product Details

Authors:
Giovanni PeccatiMurad S Taqqu
Book Format:
Hardcover
Country of Origin:
US
Date Published:
28 December 2010
Dimensions:
23.88 x 16 x 2.03 cm
ISBN-10:
8847016789
ISBN-13:
9788847016781
Language:
English
Location:
Milano
Pages:
274
Publisher:
Weight:
657.71 gm

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