| 书目名称 | Wiener Chaos: Moments, Cumulants and Diagrams | | 副标题 | A survey with Comput | | 编辑 | Giovanni Peccati,Murad S. Taqqu | | 视频video | | | 概述 | 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 a | | 丛书名称 | Bocconi & Springer Series | | 图书封面 |  | | 描述 | 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 applicationsranging from Malliavin calculus to stochastic differential equations and fromprobabilistic approximations to mathematical finance.This book is concerned with combinatorial structures arising from the studyof chaotic random variables related to infinitely divisible random measures. The combinatorial structures involved are those of partitions of finite sets, over whichMöbius 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. | | 出版日期 | Book 2011 | | 关键词 | Diagram formulae; Lattices of partitions; Limit theorems; Moments and cumulants; Wiener chaos; quantitati | | 版次 | 1 | | doi | https://doi.org/10.1007/978-88-470-1679-8 | | isbn_softcover | 978-88-470-5604-6 | | isbn_ebook | 978-88-470-1679-8Series ISSN 2039-1471 Series E-ISSN 2039-148X | | issn_series | 2039-1471 | | copyright | Springer Milan 2011 |
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发表于 2025-3-21 17:35:27
