Equations Involving Malliavin Calculus Operators Applications and Numerical Approximation /
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 o...
| Main Authors: | , |
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| Corporate Author: | |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2017.
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| Edition: | 1st ed. 2017. |
| Series: | SpringerBriefs in Mathematics,
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| Subjects: | |
| Online Access: | https://doi.org/10.1007/978-3-319-65678-6 |
Table of 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.