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Wiener Chaos: Moments, Cumulants and Diagrams

Giovanni Peccati
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      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 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.
      Format: Hardback CONTRIBUTORS: Giovanni Peccati EAN: 9788847016781 COUNTRY: Italy PAGES: WEIGHT: 606 g HEIGHT: 235 cm
      PUBLISHED BY: Springer Verlag DATE PUBLISHED: 2010-12-28 CITY: GENRE: MATHEMATICS / Applied, MATHEMATICS / Probability & Statistics / General, MATHEMATICS / Mathematical Analysis, MATHEMATICS / Combinatorics WIDTH: 155 cm SPINE:

      Book Themes:

      Economics, Finance, Business and Management, Discrete mathematics, Integral calculus and equations, Probability and statistics, Applied mathematics, Stochastics

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      Giovanni Peccati is a Professor of Stochastic Analysis and Mathematical Finance at Luxembourg University. Murad S. Taqqu is a Professor of Mathematics and Statistics at Boston University.
      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 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.
      Format: Hardback CONTRIBUTORS: Giovanni Peccati EAN: 9788847016781 COUNTRY: Italy PAGES: WEIGHT: 606 g HEIGHT: 235 cm
      PUBLISHED BY: Springer Verlag DATE PUBLISHED: 2010-12-28 CITY: GENRE: MATHEMATICS / Applied, MATHEMATICS / Probability & Statistics / General, MATHEMATICS / Mathematical Analysis, MATHEMATICS / Combinatorics WIDTH: 155 cm SPINE:

      Book Themes:

      Economics, Finance, Business and Management, Discrete mathematics, Integral calculus and equations, Probability and statistics, Applied mathematics, Stochastics

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      Giovanni Peccati is a Professor of Stochastic Analysis and Mathematical Finance at Luxembourg University. Murad S. Taqqu is a Professor of Mathematics and Statistics at Boston University.

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