Wiener chaos moments, cumulants and diagrams : a survey with computer implementation / [electronic resource] :
- 作者： Peccati, Giovanni.
- 其他作者：
- 出版： Milano : Springer Milan
- 叢書名： Bocconi & Springer series,1
- 主題： Gaussian processes. , Combinatorial analysis , Time-series analysis , Mathematics , Probability Theory and Stochastic Processes. , Combinatorics. , Measure and Integration.
- ISBN： 9788847016798 (electronic bk.) 、 9788847016781 (paper)
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FIND@SFXID:
CGU
- 資料類型: 電子書
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讀者標籤：
- 系統號： 005069706 | 機讀編目格式
館藏資訊
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.