-PDF Download- Equations Involving Malliavin Calculus Operators EBOOK

Equations Involving Malliavin Calculus Operators

Author: Tijana Levajković

Publisher: Springer

Published: 2017-08-31

Total Pages: 132

ISBN-13: 3319656783

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."

Malliavin Calculus with Applications to Stochastic Partial Differential Equations

Author: Marta Sanz-Sole

Publisher: CRC Press

Published: 2005-08-17

Total Pages: 172

ISBN-13: 1439818940

DOWNLOAD EBOOK →

Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics. This book present

The Malliavin Calculus and Related Topics

Author: David Nualart

Publisher: Springer Science & Business Media

Published: 2013-12-11

Total Pages: 273

ISBN-13: 1475724373

DOWNLOAD EBOOK →

The origin of this book lies in an invitation to give a series of lectures on Malliavin calculus at the Probability Seminar of Venezuela, in April 1985. The contents of these lectures were published in Spanish in [176]. Later these notes were completed and improved in two courses on Malliavin cal culus given at the University of California at Irvine in 1986 and at Ecole Polytechnique Federale de Lausanne in 1989. The contents of these courses correspond to the material presented in Chapters 1 and 2 of this book. Chapter 3 deals with the anticipating stochastic calculus and it was de veloped from our collaboration with Moshe Zakai and Etienne Pardoux. The series of lectures given at the Eighth Chilean Winter School in Prob ability and Statistics, at Santiago de Chile, in July 1989, allowed us to write a pedagogical approach to the anticipating calculus which is the basis of Chapter 3. Chapter 4 deals with the nonlinear transformations of the Wiener measure and their applications to the study of the Markov property for solutions to stochastic differential equations with boundary conditions.

Differentiable Measures and the Malliavin Calculus

Author: Vladimir Igorevich Bogachev

Publisher: American Mathematical Soc.

Published: 2010-07-21

Total Pages: 506

ISBN-13: 082184993X

DOWNLOAD EBOOK →

This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.

Introduction to Malliavin Calculus

Author: David Nualart

Publisher: Cambridge University Press

Published: 2018-09-27

Total Pages: 249

ISBN-13: 1107039126

DOWNLOAD EBOOK →

A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.

The Malliavin Calculus

Author: Denis R. Bell

Publisher: Courier Corporation

Published: 2012-12-03

Total Pages: 124

ISBN-13: 0486152057

DOWNLOAD EBOOK →

This introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and a variety of applications. 1987 edition.

Malliavin Calculus and Stochastic Analysis

Author: Frederi Viens

Publisher: Springer Science & Business Media

Published: 2013-02-15

Total Pages: 580

ISBN-13: 1461459060

DOWNLOAD EBOOK →

The stochastic calculus of variations of Paul Malliavin (1925 - 2010), known today as the Malliavin Calculus, has found many applications, within and beyond the core mathematical discipline. Stochastic analysis provides a fruitful interpretation of this calculus, particularly as described by David Nualart and the scores of mathematicians he influences and with whom he collaborates. Many of these, including leading stochastic analysts and junior researchers, presented their cutting-edge research at an international conference in honor of David Nualart's career, on March 19-21, 2011, at the University of Kansas, USA. These scholars and other top-level mathematicians have kindly contributed research articles for this refereed volume.

Stochastic Analysis

Author: Paul Malliavin

Publisher: Springer

Published: 2015-06-12

Total Pages: 346

ISBN-13: 3642150748

DOWNLOAD EBOOK →

In 5 independent sections, this book accounts recent main developments of stochastic analysis: Gross-Stroock Sobolev space over a Gaussian probability space; quasi-sure analysis; anticipate stochastic integrals as divergence operators; principle of transfer from ordinary differential equations to stochastic differential equations; Malliavin calculus and elliptic estimates; stochastic Analysis in infinite dimension.

Diffusions and Elliptic Operators

Author: Richard F. Bass

Publisher: Springer Science & Business Media

Published: 2006-05-11

Total Pages: 240

ISBN-13: 0387226044

DOWNLOAD EBOOK →

A discussion of the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE, and moves on to probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions. The author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators, as well as Martingale problems and the Malliavin calculus. While serving as a textbook for a graduate course on diffusion theory with applications to PDE, this will also be a valuable reference to researchers in probability who are interested in PDE, as well as for analysts interested in probabilistic methods.

Analysis of Pseudo-Differential Operators

Author: Shahla Molahajloo

Publisher: Springer

Published: 2019-05-08

Total Pages: 257

ISBN-13: 3030051684

DOWNLOAD EBOOK →

This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the session and invited papers by experts in fields that involve pseudo-differential operators. The first four chapters focus on the functional analysis of pseudo-differential operators on a spectrum of settings from Z to Rn to compact groups. Chapters 5 and 6 discuss operators on Lie groups and manifolds with edge, while the following two chapters cover topics related to probabilities. The final chapters then address topics in differential equations.