Wiener chaos : moments, cumulants and diagrams : a survey with computer implementation
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 differ...
Guardat en:
| Autors principals: | , |
|---|---|
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
Milano :
Springer Milan : Springer e-books
[20..].
Cham : Springer Nature |
| Col·lecció: | Bocconi & Springer Series
1 |
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Description d'après consultation du 26 février 2013 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Wiener chaos, moments, cumulants and diagrams, a survey with computer implementation, Giovanni Peccati, Murad S. Taqqu, 2011, Milan, Bocconi University Press, Springer, 1 vol.(XIII-274 p.), Bocconi & Springer series, 978-88-470-1678-1 |
| Sumari: | 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 |
|---|---|
| Descripció de l’ítem: | Description d'après consultation du 26 février 2013 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografia: | Bibliogr. Index |
| ISBN: | 9788847016798 |
| ISSN: | 2039-1471 |
| Accés: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |