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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)

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
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.".--
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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)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-65678-6
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
Control code
978-3-319-65678-6
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, non-commercial 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
10.1007/978-3-319-65678-6
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)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-65678-6
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
Control code
978-3-319-65678-6
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, non-commercial 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
10.1007/978-3-319-65678-6
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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