The Resource Equations involving Malliavin calculus operators : applications and numerical approximation, by Tijana Levajković, Hermann Mena, (electronic resource)
Equations involving Malliavin calculus operators : applications and numerical approximation, by Tijana Levajković, Hermann Mena, (electronic resource)
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The item Equations involving Malliavin calculus operators : applications and numerical approximation, by Tijana Levajković, Hermann Mena, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Equations involving Malliavin calculus operators : applications and numerical approximation, by Tijana Levajković, Hermann Mena, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 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 readerfriendly. 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 OrnsteinUhlenbeck 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.".
 Language
 eng
 Extent
 1 online resource (X, 132 pages)
 Contents

 1 White Noise Analysis and Chaos Expansions: 1.1 Introduction. 1.3 Deterministic background. 1.2 Spaces of random variables. 1.4 Stochastic processes. 1.5 Operators
 References. 2 Generalized Operators of Malliavin Calculus: 2.1 Introduction. 2.1 The Malliavin derivative. 2.2 The Skorokhod integral. 2.3 The OrnsteinUhlenbeck operator. 2.4 Properties of the Malliavin operators. 2.5 Fractional operators of the Malliavin calculus
 References. 3 Equations involving Mallivin Calculus Operators: 3.1 Introduction
 3.2 Equations with the OrnsteinUhlenbeck operator. 3.3 First order equation with the Malliavin derivative operator. 3.4 Nonhomogeneous equation with the Malliavin derivative operator. 3.5 Wicktype equations involving the Malliavin derivative. 3.6 Integral equation. References
 4 Applications and Numerical Approximation: 4.1 Introduction. 4.1 A stochastic optimal control problem. 4.3 Operator differential algebraic equations. 4.4 Stationary equations. 4.5 A fractional optimal control problem. 4.6 Numerical approximation. References
 Isbn
 9783319656786
 Label
 Equations involving Malliavin calculus operators : applications and numerical approximation
 Title
 Equations involving Malliavin calculus operators
 Title remainder
 applications and numerical approximation
 Statement of responsibility
 by Tijana Levajković, Hermann Mena
 Language
 eng
 Summary
 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 readerfriendly. 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 OrnsteinUhlenbeck 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.".
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Levajković, Tijana
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Mena, Hermann.
 Series statement

 Springer eBooks
 SpringerBriefs in Mathematics,
 http://library.link/vocab/subjectName

 Mathematics
 Functional analysis
 Numerical analysis
 Calculus of variations
 Probabilities
 Label
 Equations involving Malliavin calculus operators : applications and numerical approximation, by Tijana Levajković, Hermann Mena, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1 White Noise Analysis and Chaos Expansions: 1.1 Introduction. 1.3 Deterministic background. 1.2 Spaces of random variables. 1.4 Stochastic processes. 1.5 Operators  References. 2 Generalized Operators of Malliavin Calculus: 2.1 Introduction. 2.1 The Malliavin derivative. 2.2 The Skorokhod integral. 2.3 The OrnsteinUhlenbeck operator. 2.4 Properties of the Malliavin operators. 2.5 Fractional operators of the Malliavin calculus  References. 3 Equations involving Mallivin Calculus Operators: 3.1 Introduction  3.2 Equations with the OrnsteinUhlenbeck operator. 3.3 First order equation with the Malliavin derivative operator. 3.4 Nonhomogeneous equation with the Malliavin derivative operator. 3.5 Wicktype equations involving the Malliavin derivative. 3.6 Integral equation. References  4 Applications and Numerical Approximation: 4.1 Introduction. 4.1 A stochastic optimal control problem. 4.3 Operator differential algebraic equations. 4.4 Stationary equations. 4.5 A fractional optimal control problem. 4.6 Numerical approximation. References
 Control code
 9783319656786
 Dimensions
 unknown
 Extent
 1 online resource (X, 132 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319656786
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319656786
 Other physical details
 7 illustrations, 6 illustrations in color.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1003106683
 Label
 Equations involving Malliavin calculus operators : applications and numerical approximation, by Tijana Levajković, Hermann Mena, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1 White Noise Analysis and Chaos Expansions: 1.1 Introduction. 1.3 Deterministic background. 1.2 Spaces of random variables. 1.4 Stochastic processes. 1.5 Operators  References. 2 Generalized Operators of Malliavin Calculus: 2.1 Introduction. 2.1 The Malliavin derivative. 2.2 The Skorokhod integral. 2.3 The OrnsteinUhlenbeck operator. 2.4 Properties of the Malliavin operators. 2.5 Fractional operators of the Malliavin calculus  References. 3 Equations involving Mallivin Calculus Operators: 3.1 Introduction  3.2 Equations with the OrnsteinUhlenbeck operator. 3.3 First order equation with the Malliavin derivative operator. 3.4 Nonhomogeneous equation with the Malliavin derivative operator. 3.5 Wicktype equations involving the Malliavin derivative. 3.6 Integral equation. References  4 Applications and Numerical Approximation: 4.1 Introduction. 4.1 A stochastic optimal control problem. 4.3 Operator differential algebraic equations. 4.4 Stationary equations. 4.5 A fractional optimal control problem. 4.6 Numerical approximation. References
 Control code
 9783319656786
 Dimensions
 unknown
 Extent
 1 online resource (X, 132 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319656786
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319656786
 Other physical details
 7 illustrations, 6 illustrations in color.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1003106683
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