Téléchargez le livre : Equations Involving Malliavin Calculus Operators

Equations Involving Malliavin Calculus Operators

Applications and Numerical Approximation

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Éditeur :

Springer


Collection :

SpringerBriefs in Mathematics

Paru le : 2017-08-31



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Description

This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion representation of stochastic processes and its application for solving several classes of stochastic differential equations with singular data involving the main operators of Malliavin calculus. In addition, applications in optimal control and numerical approximations are discussed. 
The book is divided into four chapters. The first, entitled White Noise Analysis and Chaos Expansions, includes notation and provides the reader with the theoretical background needed to understand the subsequent chapters. 
In Chapter 2, Generalized Operators of Malliavin Calculus, the Malliavin derivative operator, the Skorokhod integraland the Ornstein-Uhlenbeck operator are introduced in terms of chaos expansions. The main properties of the operators, which are known in the literature for the square integrable processes, are proven using the chaos expansion approach and extended for generalized and test stochastic processes. 

Chapter 3, Equations involving Malliavin Calculus operators, is devoted to the study of several types of stochastic differential equations that involve the operators of Malliavin calculus, introduced in the previous chapter. Fractional versions of these operators are also discussed.Finally, in Chapter 4, Applications and Numerical Approximations are discussed. Specifically, we consider the stochastic linear quadratic optimal control problem with different forms of noise disturbances, operator differential algebraic equations arising in fluid dynamics, stationary equations and fractional versions of the equations studied – applications never covered in the extant literature. Moreover, numerical validations of the method are provided for specific problems."
Pages
132 pages
Collection
SpringerBriefs in Mathematics
Parution
2017-08-31
Marque
Springer
EAN papier
9783319656779
EAN PDF
9783319656786
Informations sur l'ebook
Nombre pages copiables
1
Nombre pages imprimables
13
Taille du fichier
2990 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
58,01 €
EAN EPUB
9783319656786
Informations sur l'ebook
Nombre pages copiables
1
Nombre pages imprimables
13
Taille du fichier
4342 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
58,01 €

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