Equations Involving Malliavin Calculus Operators : Applications and Numerical Approximation. 1st ed. 2017

種類:

電子ブック

責任表示:

by Tijana Levajković, Hermann Mena

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Levajković, Tijana.
• Mena, Hermann.
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Mathematics ;

ISBN:

9783319656786 [3319656783]    

注記:

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
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

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