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