{"product_id":"9788847016781","title":"Wiener Chaos: Moments, Cumulants and Diagrams: A survey with Computer Implementation","description":"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.\u003cbr\u003eThis book is concerned with combinatorial structures arising from the study of chaotic random variables related to infinitely divisible random measures. \u003cbr\u003eThe combinatorial structures involved are those of partitions of finite sets, \u003cbr\u003eover which Möbius functions and related inversion formulae are defined. \u003cbr\u003eThis combinatorial standpoint (which is originally due to Rota and Wallstrom) \u003cbr\u003eprovides an ideal framework for diagrams, which are graphical devices used to compute moments and cumulants of random variables.\u003cbr\u003eSeveral applications are described, in particular, recent limit theorems for chaotic random variables. \u003cbr\u003eAn Appendix presents a computer implementation in MATHEMATICA for many of the formulae.","brand":"Springer Milan","offers":[{"title":"Default Title","offer_id":47053001818352,"sku":"9788847016781","price":139.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9788847016781_p0.jpg?v=1763753806","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9788847016781","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}