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Wiener Chaos: Moments, Cumulants and Diagrams - A survey with Computer Implementation (Hardcover, 2011)
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Wiener Chaos: Moments, Cumulants and Diagrams - A survey with Computer Implementation (Hardcover, 2011)
Series: Bocconi & Springer Series, 1
Expected to ship within 10 - 15 working days
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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 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 M bius 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
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