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Equations Involving Malliavin Calculus Operators: Applications and Numerical Approximation - Couverture souple
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Synopsis
Friendly approach for solving stochastic equations with singular data
Novel applications of operators of the Malliavin calculus
From theoretical to numerical results of SPDEs with singular data
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
À propos de l'auteur
Tijana Levajkovic is currently a postdoctoral researcher at the at the Department of Mathematics, University of Innsbruck. Her main research interests are in the fields of functional and stochastic analysis, particularly in infinite dimensional stochastic analysis, white noise analysis, Maliavin calculus, generalized stochastic processes, stochastic partial differential equations, algebras of generalized functions and optimal control.
Hermann Mena is professor at Yachay Tech, Ecuador. He also has an affiliation at the Department of Mathematics of Univeristy of Innsbruck, Austria. His research interests include applied mathematics, numerical analysis and optimal control. Particularly, deterministic and stochastic optimal control theory, numerical methods for optimal control problems and uncertainty quantification.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Equations Involving Malliavin Calculus Operators (eng)
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Equations Involving Malliavin Calculus Operators : Applications and Numerical Approximation
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Equations Involving Malliavin Calculus Operators : Applications and Numerical Approximation
Edité par
Springer, 2017
ISBN 10 : 3319656775
ISBN 13 : 9783319656779
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Equations Involving Malliavin Calculus Operators
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Berlin Springer International Publishing Springer Sep 2017, 2017
ISBN 10 : 3319656775
ISBN 13 : 9783319656779
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 integral and 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.' 132 pp. Englisch. N° de réf. du vendeur 9783319656779
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Equations Involving Malliavin Calculus Operators : Applications and Numerical Approximation
Edité par
Springer, 2017
ISBN 10 : 3319656775
ISBN 13 : 9783319656779
Ancien ou d'occasion
Couverture souple
Vendeur : GreatBookPricesUK, Woodford Green, Royaume-Uni
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Equations Involving Malliavin Calculus Operators: Applications and Numerical Approximation
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Equations Involving Malliavin Calculus Operators : Applications and Numerical Approximation
Edité par
Springer, Berlin, Springer, 2017
ISBN 10 : 3319656775
ISBN 13 : 9783319656779
Neuf
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Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.'. N° de réf. du vendeur 9783319656779
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