{"product_id":"wiener-chaos-moments-cumulants-and-diagram-formulae-a-survey-with-computer-implementation-von-giovanni-peccati-murad-s-taqqu","title":"Wiener Chaos: Moments, Cumulants and Diagrams","description":"The concept of Wiener chaos generalizes to an infinite-dimensional setting the \nproperties of orthogonal polynomials associated with probability distributions \non the real line. It plays a crucial role in modern probability theory, with applications\nranging from Malliavin calculus to stochastic differential equations and from\nprobabilistic approximations to mathematical finance.\nThis book is concerned with combinatorial structures arising from the study\nof chaotic random variables related to infinitely divisible random measures. \nThe combinatorial structures involved are those of partitions of finite sets, \nover which  Möbius functions and related inversion formulae are defined. \nThis combinatorial standpoint (which is originally due to Rota and Wallstrom) \nprovides an ideal framework for diagrams, which are graphical devices used \nto compute moments and cumulants of random variables.\nSeveral applications are described, in particular, recent limit theorems for chaotic random variables.  \nAn Appendix presents a computer implementation in MATHEMATICA for many of the formulae.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9788847056046\"\u003e\u003ch3\u003eA survey with Computer Implementation\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9788847016781\"\u003e\u003ch3\u003eA survey with Computer Implementation\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9788847056046","offer_id":39466008674397,"sku":"9788847056046","price":53.49,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9788847016781","offer_id":40567760912477,"sku":"9788847016781","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/9496af12-0c41-401b-ad03-07f2ca9f8f7f.jpg?v=1775192763","url":"https:\/\/shop.autorenwelt.de\/products\/wiener-chaos-moments-cumulants-and-diagram-formulae-a-survey-with-computer-implementation-von-giovanni-peccati-murad-s-taqqu","provider":"Autorenwelt Shop","version":"1.0","type":"link"}