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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)
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 Boston University Libraries.This item is available to borrow from all library branches.
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 Boston University Libraries.
This item is available to borrow from all library branches.
 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
 X, 132 p. 7 illus., 6 illus. in color.
 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
 Subject

 Probability Theory and Stochastic Processes
 Numerical Analysis
 Functional analysis
 Probabilities
 Differential equations, Partial
 Functional Analysis
 Probabilities
 Numerical analysis
 Calculus of variations
 Electronic resources
 Functional Analysis
 Numerical analysis
 Mathematics
 Differential equations, Partial
 Partial Differential Equations
 Mathematics
 Calculus of Variations and Optimal Control; Optimization
 Numerical Analysis
 Functional analysis
 Calculus of variations
 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."
 http://library.link/vocab/creatorName
 Levajkovic, Tijana
 Image bit depth
 0
 LC call number

 QA273.A1274.9
 QA274274.9
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Mena, Hermann
 SpringerLink
 Series statement
 SpringerBriefs in Mathematics,
 http://library.link/vocab/subjectName

 Mathematics
 Functional analysis
 Differential equations, Partial
 Numerical analysis
 Calculus of variations
 Probabilities
 Mathematics
 Probability Theory and Stochastic Processes
 Functional Analysis
 Partial Differential Equations
 Calculus of Variations and Optimal Control; Optimization
 Numerical Analysis
 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
 Dimensions
 unknown
 Extent
 X, 132 p. 7 illus., 6 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 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
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319656786
 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
 Dimensions
 unknown
 Extent
 X, 132 p. 7 illus., 6 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 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
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319656786
Subject
 Calculus of Variations and Optimal Control; Optimization
 Calculus of variations
 Calculus of variations
 Differential equations, Partial
 Differential equations, Partial
 Electronic resources
 Functional Analysis
 Functional Analysis
 Functional analysis
 Functional analysis
 Mathematics
 Mathematics
 Numerical Analysis
 Numerical Analysis
 Numerical analysis
 Numerical analysis
 Partial Differential Equations
 Probabilities
 Probabilities
 Probability Theory and Stochastic Processes
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