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)

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
Creator
Contributor
Author
Provider
Subject
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 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."
Member of
http://library.link/vocab/creatorName
Levajkovic, Tijana
Image bit depth
0
LC call number
  • QA273.A1-274.9
  • QA274-274.9
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)
Instantiates
Publication
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 Ornstein-Uhlenbeck 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 Ornstein-Uhlenbeck operator.- 3.3 First order equation with the Malliavin derivative operator.- 3.4 Nonhomogeneous equation with the Malliavin derivative operator.- 3.5 Wick-type 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
10.1007/978-3-319-65678-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-65678-6
Label
Equations Involving Malliavin Calculus Operators : Applications and Numerical Approximation, by Tijana Levajković, Hermann Mena, (electronic resource)
Publication
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 Ornstein-Uhlenbeck 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 Ornstein-Uhlenbeck operator.- 3.3 First order equation with the Malliavin derivative operator.- 3.4 Nonhomogeneous equation with the Malliavin derivative operator.- 3.5 Wick-type 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
10.1007/978-3-319-65678-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-65678-6

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