---

＜電子ブック＞
Wiener Chaos: Moments, Cumulants and Diagrams : A survey with Computer Implementation / by Giovanni Peccati, Murad S. Taqqu
(Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics. ISSN:2039148X ; 1)

版	1st ed. 2011.
出版者	(Milano : Springer Milan : Imprint: Springer)
出版年	2011
本文言語	英語
大きさ	XIII, 274 p : online resource
著者標目	*Peccati, Giovanni author Taqqu, Murad S author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Social sciences -- Mathematics  全ての件名で検索 LCSH:Discrete mathematics LCSH:Measure theory FREE:Probability Theory FREE:Mathematics in Business, Economics and Finance FREE:Discrete Mathematics FREE:Measure and Integration
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-88-470-1679-8

 類似資料