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Wiener Chaos: Moments, Cumulants and Diagrams

Wiener Chaos: Moments, Cumulants and Diagrams

A survey with Computer Implementation

by Giovanni Peccati and Murad S. Taqqu
Paperback
Publication Date: 12/10/2014
  $155.40
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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 Moebius 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.
ISBN:
9788847056046
9788847056046
Category:
Probability & statistics
Format:
Paperback
Publication Date:
12-10-2014
Publisher:
Springer Verlag
Country of origin:
Italy
Pages:
274
Dimensions (mm):
235x155x15mm
Weight:
0.45kg

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