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Degenerate Stochastic Differential Equations and Hypoellipticity

1996-05-15 Mathematics
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Release : 1996-05-15
Genre : Mathematics
Kind : eBook
Book Rating : 898/5 ( reviews)

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Book Synopsis Degenerate Stochastic Differential Equations and Hypoellipticity by : Denis Bell

Download or read book Degenerate Stochastic Differential Equations and Hypoellipticity written by Denis Bell. This book was released on 1996-05-15. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this Monograph is the study of degenerate stochastic differential equations, considered as transformations of the Wiener measure, and their relationship with partial differential equations. The book contains an elementary derivation of Malliavin's integration by parts formula, a proof of the probabilistic form of Hormander's theorem, an extension of Hormander's theorem for infinitely degenerate differential operators, and criteria for the regularity of measures induced by stochastic hereditary-delay equations.

Real and Stochastic Analysis

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 548/5 ( reviews)

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Book Synopsis Real and Stochastic Analysis by : M. M. Rao

Download or read book Real and Stochastic Analysis written by M. M. Rao. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: As in the case of the two previous volumes published in 1986 and 1997, the purpose of this monograph is to focus the interplay between real (functional) analysis and stochastic analysis show their mutual benefits and advance the subjects. The presentation of each article, given as a chapter, is in a research-expository style covering the respective topics in depth. In fact, most of the details are included so that each work is essentially self contained and thus will be of use both for advanced graduate students and other researchers interested in the areas considered. Moreover, numerous new problems for future research are suggested in each chapter. The presented articles contain a substantial number of new results as well as unified and simplified accounts of previously known ones. A large part of the material cov ered is on stochastic differential equations on various structures, together with some applications. Although Brownian motion plays a key role, (semi-) martingale theory is important for a considerable extent. Moreover, noncommutative analysis and probabil ity have a prominent role in some chapters, with new ideas and results. A more detailed outline of each of the articles appears in the introduction and outline to assist readers in selecting and starting their work. All chapters have been reviewed.

Differentiable Measures and the Malliavin Calculus

2010-07-21 Mathematics
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Release : 2010-07-21
Genre : Mathematics
Kind : eBook
Book Rating : 93X/5 ( reviews)

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Book Synopsis Differentiable Measures and the Malliavin Calculus by : Vladimir Igorevich Bogachev

Download or read book Differentiable Measures and the Malliavin Calculus written by Vladimir Igorevich Bogachev. This book was released on 2010-07-21. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Differential Equations and Applications

2014-06-20 Mathematics
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Release : 2014-06-20
Genre : Mathematics
Kind : eBook
Book Rating : 876/5 ( reviews)

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Book Synopsis Stochastic Differential Equations and Applications by : Avner Friedman

Download or read book Stochastic Differential Equations and Applications written by Avner Friedman. This book was released on 2014-06-20. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Differential Equations and Applications, Volume 1 covers the development of the basic theory of stochastic differential equation systems. This volume is divided into nine chapters. Chapters 1 to 5 deal with the basic theory of stochastic differential equations, including discussions of the Markov processes, Brownian motion, and the stochastic integral. Chapter 6 examines the connections between solutions of partial differential equations and stochastic differential equations, while Chapter 7 describes the Girsanov’s formula that is useful in the stochastic control theory. Chapters 8 and 9 evaluate the behavior of sample paths of the solution of a stochastic differential system, as time increases to infinity. This book is intended primarily for undergraduate and graduate mathematics students.

Stochastic Analysis and Related Topics VI

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 22X/5 ( reviews)

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Book Synopsis Stochastic Analysis and Related Topics VI by : Laurent Decreusefond

Download or read book Stochastic Analysis and Related Topics VI written by Laurent Decreusefond. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the contributions of the participants of the Sixth Oslo-Silivri Workshop on Stochastic Analysis, held in Geilo from July 29 to August 6, 1996. There are two main lectures " Stochastic Differential Equations with Memory, by S.E.A. Mohammed, " Backward SDE's and Viscosity Solutions of Second Order Semilinear PDE's, by E. Pardoux. The main lectures are presented at the beginning of the volume. There is also a review paper at the third place about the stochastic calculus of variations on Lie groups. The contributing papers vary from SPDEs to Non-Kolmogorov type probabilistic models. We would like to thank " VISTA, a research cooperation between Norwegian Academy of Sciences and Letters and Den Norske Stats Oljeselskap (Statoil), " CNRS, Centre National de la Recherche Scientifique, " The Department of Mathematics of the University of Oslo, " The Ecole Nationale Superieure des Telecommunications, for their financial support. L. Decreusefond J. Gjerde B. 0ksendal A.S. Ustunel PARTICIPANTS TO THE 6TH WORKSHOP ON STOCHASTIC ANALYSIS Vestlia HØyfjellshotell, Geilo, Norway, July 28 -August 4, 1996. E-mail: [email protected] Aureli ALABERT Departament de Matematiques Laurent DECREUSEFOND Universitat Autonoma de Barcelona Ecole Nationale Superieure des Telecom 08193-Bellaterra munications CATALONIA (Spain) Departement Reseaux E-mail: [email protected] 46, rue Barrault Halvard ARNTZEN 75634 Paris Cedex 13 Dept. of Mathematics FRANCE University of Oslo E-mail: [email protected] Box 1053 Blindern Laurent DENIS N-0316 Oslo C.M.I

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