Author: Horst Osswald
Publisher: Cambridge University Press
ISBN: 1107016142
Category : Mathematics
Languages : en
Pages : 429
Get Book
Book Description
After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.
Author: Horst Osswald
Publisher:
ISBN: 9781139233842
Category : MATHEMATICS
Languages : en
Pages : 430
Get Book
Book Description
Assuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard analysis, which allows infinite-dimensional problems to be treated as finite-dimensional. The result is an intuitive, indeed enjoyable, development of both Malliavin calculus and nonstandard analysis. The main aspects of stochastic analysis and Malliavin calculus are incorporated into this simplifying framework. Topics covered include Brownian motion, Ornstein-Uhlenbeck processes both with values in abstract Wiener spaces, Levy processes, multiple stochastic integrals, chaos decomposition, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes and Girsanov transformations. The careful exposition, which is neither too abstract nor too theoretical, makes this book accessible to graduate students, as well as to researchers interested in the techniques.
Author: Horst Osswald
Publisher:
ISBN: 9781139230858
Category : Brownian motion processes
Languages : en
Pages :
Get Book
Book Description
"Assuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard analysis, which allows infinite-dimensional problems to be treated as finite-dimensional. The result is an intuitive, indeed enjoyable, development of both Malliavin calculus and nonstandard analysis. The main aspects of stochastic analysis and Malliavin calculus are incorporated into this simplifying framework. Topics covered include Brownian motion, Ornstein-Uhlenbeck processes both with values in abstract Wiener spaces, Lévy processes, multiple stochastic integrals, chaos decomposition, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes and Girsanov transformations. The careful exposition, which is neither too abstract nor too theoretical, makes this book accessible to graduate students, as well as to researchers interested in the techniques"--
Author: Denis R. Bell
Publisher: Courier Corporation
ISBN: 0486152057
Category : Mathematics
Languages : en
Pages : 124
Get Book
Book Description
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.
Author: Nasir Uddin Ahmed
Publisher: World Scientific
ISBN: 9814366366
Category : Mathematics
Languages : en
Pages : 314
Get Book
Book Description
This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process ? covering the classical Wiener?Ito class including the generalized functionals of Hida as special cases, among others. It presents a thorough and comprehensive treatment of the Wiener?Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems.Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated Riesz?Fischer theorem for separable Hilbert spaces and the space of Wiener?Ito functionals is drawn out, thus providing a clear insight into the subject.
Author: H Kunita
Publisher: CRC Press
ISBN: 9780582244900
Category : Mathematics
Languages : en
Pages : 340
Get Book
Book Description
The book discusses the following topics in stochastic analysis: 1. Stochastic analysis related to Lie groups: stochastic analysis of loop spaces and infinite dimensional manifolds has been developed rapidly after the fundamental works of Gross and Malliavin. (Lectures by Driver, Gross, Mitoma, and Sengupta.)
Author: Peter A. Loeb
Publisher: Springer
ISBN: 9401773270
Category : Mathematics
Languages : en
Pages : 481
Get Book
Book Description
Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; it is often used as a ‘secret weapon’ by those who know the technique. This book illuminates the subject with some of the most striking applications in analysis, topology, functional analysis, probability and stochastic analysis, as well as applications in economics and combinatorial number theory. The first chapter is designed to facilitate the beginner in learning this technique by starting with calculus and basic real analysis. The second chapter provides the reader with the most important tools of nonstandard analysis: the transfer principle, Keisler’s internal definition principle, the spill-over principle, and saturation. The remaining chapters of the book study different fields for applications; each begins with a gentle introduction before then exploring solutions to open problems. All chapters within this second edition have been reworked and updated, with several completely new chapters on compactifications and number theory. Nonstandard Analysis for the Working Mathematician will be accessible to both experts and non-experts, and will ultimately provide many new and helpful insights into the enterprise of mathematics.
Author: Laurent Decreusefond
Publisher: Springer Science & Business Media
ISBN: 9780817642006
Category : Mathematics
Languages : en
Pages : 266
Get Book
Book Description
One of the most challenging subjects of stochastic analysis in relation to physics is the analysis of heat kernels on infinite dimensional manifolds. The simplest nontrivial case is that of thepath and loop space on a Lie group. In this volume an up-to-date survey of the topic is given by Leonard Gross, a prominent developer of the theory. Another concise but complete survey of Hausdorff measures on Wiener space and its applications to Malliavin Calculus is given by D. Feyel, one of the most active specialists in this area. Other survey articles deal with short-time asymptotics of diffusion pro cesses with values in infinite dimensional manifolds and large deviations of diffusions with discontinuous drifts. A thorough survey is given of stochas tic integration with respect to the fractional Brownian motion, as well as Stokes' formula for the Brownian sheet, and a new version of the log Sobolev inequality on the Wiener space. Professional mathematicians looking for an overview of the state-of-the art in the above subjects will find this book helpful. In addition, graduate students as well as researchers whose domain requires stochastic analysis will find the original results of interest for their own research. The organizers acknowledge gratefully the financial help ofthe University of Oslo, and the invaluable aid of Professor Bernt 0ksendal and l'Ecole Nationale Superieure des Telecommunications.
Author: Giulia Di Nunno
Publisher: Springer Science & Business Media
ISBN: 3540785728
Category : Mathematics
Languages : en
Pages : 418
Get Book
Book Description
This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.
Author: Ivan Nourdin
Publisher: Cambridge University Press
ISBN: 1107017777
Category : Mathematics
Languages : en
Pages : 255
Get Book
Book Description
This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.
