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Autore: | Ahmed N. U (Nasir Uddin) |
Titolo: | Generalized functionals of Brownian motion and their applications [[electronic resource] ] : nonlinear functionals of fundamental stochastic processes / / N.U. Ahmed |
Pubblicazione: | Singapore ; ; Hackensack, : World Scientific, c2012 |
Descrizione fisica: | 1 online resource (314 p.) |
Disciplina: | 515.3 |
Soggetto topico: | Brownian motion processes |
Stochastic processes | |
Note generali: | Description based upon print version of record. |
Nota di bibliografia: | Includes bibliographical references (p. 291-296) and index. |
Nota di contenuto: | Preface; Contents; 1. Background Material; 1.1 Introduction; 1.2 Wiener Process and Wiener Measure; 1.3 Stochastic Differential Equations in Rd; 1.4 Stochastic Differential Equations in H; 1.4.1 Measure Solutions; 1.5 Nonlinear Filtering; 1.5.1 Finite Dimensional Filtering; 1.5.2 Infinite Dimensional Filtering; 1.6 Elements of Vector Measures; 1.7 Some Problems for Exercise; 2. Regular Functionals of Brownian Motion; 2.1 Introduction; 2.2 Functionals of Scalar Brownian Motion; 2.3 Functionals of Vector Brownian Motion; 2.4 Functionals of Gaussian Random Field (GRF) |
5.6 Some Problems for Exercise6. Lp-Based Generalized Functionals of White Noise III; 6.1 Introduction; 6.2 Homogeneous Functionals of Degree n; 6.3 Nonhomogeneous Functionals; 6.4 Weighted Generalized Functionals; 6.5 Some Examples Related to Section 6.4; 6.6 Generalized Functionals of Random Fields Applied; 6.7 ̃ Fq-Valued Vector Measures with Application; 6.8 Some Problems for Exercise; 7. Wp,m-Based Generalized Functionals of White Noise IV; 7.1 Introduction; 7.2 Homogeneous Functionals; 7.3 Nonhomogeneous Functionals; 7.4 Inductive and Projective Limits | |
8.7.2 Smoothness under H ̈ormander's Conditions | |
Sommario/riassunto: | This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener-Ito class including the generalized functionals of Hida as special cases, among others. It presents a thorough and comprehensive treatment of the Wiener-Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develop |
Titolo autorizzato: | Generalized functionals of Brownian motion and their applications |
ISBN: | 1-280-37753-4 |
9786613555441 | |
981-4366-37-4 | |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910778809703321 |
Lo trovi qui: | Univ. Federico II |
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