Overview
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 integraland 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.""
Full Product Details
Author: Tijana Levajković ,
Hermann Mena
Publisher: Springer International Publishing AG
Imprint: Springer International Publishing AG
Edition: 1st ed. 2017
Weight: 2.292kg
ISBN: 9783319656779
ISBN 10: 3319656775
Pages: 132
Publication Date: 11 September 2017
Audience:
College/higher education
,
Professional and scholarly
,
Undergraduate
,
Postgraduate, Research & Scholarly
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
This book aims to give a unified introduction to stochasatic differential equations involving Malliavin calculus operators. The intended audience is that of researchers and graduate students interested in stochastic partial differential equations and related fields. (John Masson Noble, Mathematical Reviews, June, 2018)
Author Information
Tijana Levajković is currently a postdoctoral researcher at the at the Department of Mathematics, University of Innsbruck. Her main research interests are in the fields of functional and stochastic analysis, particularly in infinite dimensional stochastic analysis, white noise analysis, Maliavin calculus, generalized stochastic processes, stochastic partial differential equations, algebras of generalized functions and optimal control. Hermann Mena is professor at Yachay Tech, Ecuador. He also has an affiliation at the Department of Mathematics of Univeristy of Innsbruck, Austria. His research interests include applied mathematics, numerical analysis and optimal control. Particularly, deterministic and stochastic optimal control theory, numerical methods for optimal control problems and uncertainty quantification.
