Equations Involving Malliavin Calculus Operators : Applications and Numerical Approximation
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The work Equations Involving Malliavin Calculus Operators : Applications and Numerical Approximation represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Equations Involving Malliavin Calculus Operators : Applications and Numerical Approximation
Resource Information
The work Equations Involving Malliavin Calculus Operators : Applications and Numerical Approximation represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Equations Involving Malliavin Calculus Operators : Applications and Numerical Approximation
 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."
 Image bit depth
 0
 LC call number

 QA273.A1274.9
 QA274274.9
 Literary form
 non fiction
 Series statement
 SpringerBriefs in Mathematics,
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