Download or read book Semimartingales and Their Stochastic Calculus on Manifolds written by Laurent Schwartz and published by Les Presses de L'Universite de Montreal. This book was released on 1984 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Calculus in Manifolds written by Michel Emery and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressed to both pure and applied probabilitists, including graduate students, this text is a pedagogically-oriented introduction to the Schwartz-Meyer second-order geometry and its use in stochastic calculus. P.A. Meyer has contributed an appendix: "A short presentation of stochastic calculus" presenting the basis of stochastic calculus and thus making the book better accessible to non-probabilitists also. No prior knowledge of differential geometry is assumed of the reader: this is covered within the text to the extent. The general theory is presented only towards the end of the book, after the reader has been exposed to two particular instances - martingales and Brownian motions - in manifolds. The book also includes new material on non-confluence of martingales, s.d.e. from one manifold to another, approximation results for martingales, solutions to Stratonovich differential equations. Thus this book will prove very useful to specialists and non-specialists alike, as a self-contained introductory text or as a compact reference.

Download or read book Semimartingales and Their Stochastic Calculus on Manifolds written by I. Iscoe and published by . This book was released on 1984 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Analysis on Manifolds written by Elton P. Hsu and published by American Mathematical Soc.. This book was released on 2002 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mainly from the perspective of a probabilist, Hsu shows how stochastic analysis and differential geometry can work together for their mutual benefit. He writes for researchers and advanced graduate students with a firm foundation in basic euclidean stochastic analysis, and differential geometry. He does not include the exercises usual to such texts, but does provide proofs throughout that invite readers to test their understanding. Annotation copyrighted by Book News Inc., Portland, OR.

Download or read book Semimartingale Theory and Stochastic Calculus written by Sheng-wu He and published by Taylor & Francis. This book was released on 1992 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Mechanics written by Folkert Kuipers and published by Springer Nature. This book was released on 2023-05-31 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic mechanics is a theory that holds great promise in resolving the mathematical and interpretational issues encountered in the canonical and path integral formulations of quantum theories. It provides an equivalent formulation of quantum theories, but substantiates it with a mathematically rigorous stochastic interpretation by means of a stochastic quantization prescription. The book builds on recent developments in this theory, and shows that quantum mechanics can be unified with the theory of Brownian motion in a single mathematical framework. Moreover, it discusses the extension of the theory to curved spacetime using second order geometry, and the induced Itô deformations of the spacetime symmetries. The book is self-contained and provides an extensive review of stochastic mechanics of the single spinless particle. The book builds up the theory on a step by step basis. It starts, in chapter 2, with a review of the classical particle subjected to scalar and vector potentials. In chapter 3, the theory is extended to the study of a Brownian motion in any potential, by the introduction of a Gaussian noise. In chapter 4, the Gaussian noise is complexified. The result is a complex diffusion theory that contains both Brownian motion and quantum mechanics as a special limit. In chapters 5, the theory is extended to relativistic diffusion theories. In chapter 6, the theory is further generalized to the context of pseudo-Riemannian geometry. Finally, in chapter 7, some interpretational aspects of the stochastic theory are discussed in more detail. The appendices concisely review relevant notions from probability theory, stochastic processes, stochastic calculus, stochastic differential geometry and stochastic variational calculus. The book is aimed at graduate students and researchers in theoretical physics and applied mathematics with an interest in the foundations of quantum theory and Brownian motion. The book can be used as reference material for courses on and further research in stochastic mechanics, stochastic quantization, diffusion theories on curved spacetimes and quantum gravity.

Download or read book Lectures on Probability Theory and Statistics written by M. Emery and published by Springer. This book was released on 2007-05-06 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures given at the Saint-Flour Summer School of Probability Theory during 17th Aug. - 3rd Sept. 1998. The contents of the three courses are the following: - Continuous martingales on differential manifolds. - Topics in non-parametric statistics. - Free probability theory. The reader is expected to have a graduate level in probability theory and statistics. This book is of interest to PhD students in probability and statistics or operators theory as well as for researchers in all these fields. The series of lecture notes from the Saint-Flour Probability Summer School can be considered as an encyclopedia of probability theory and related fields.

Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer Nature. This book was released on 2023-01-29 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop "Lie Theory and Its Applications in Physics" held in Sofia, Bulgaria (on-line) in June 2021. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a big interdisciplinary and interrelated field. The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Download or read book Global and Stochastic Analysis with Applications to Mathematical Physics written by Yuri E. Gliklikh and published by Springer Science & Business Media. This book was released on 2010-12-07 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems. This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation. Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics. A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.

Download or read book Stochastic Integration and Differential Equations written by Philip Protter and published by Springer. This book was released on 2013-12-21 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emery’s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.

Download or read book Seminar on Stochastic Processes 1988 written by Cinlar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1988 Seminar on Stochastic Processes was held at the University of Florida, Gainesville, March 3 through March 5, 1988. It was the eighth seminar in a continuing series of meetings which provide opportunities for researchers to discuss current work in stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Princeton University, Northwestern University, the University of Florida and the University of Virginia. The participants' enthusiasm and interest have created stimulating and successful seminars. We thank those participants who have permitted us to publish their research in this volume. This year's invited participants included B. Atkinson, J. Azema, D. Bakry, P. Baxendale, J. Brooks, G. Brosamler, K. Burdzy, E. Cinlar, R. Darling, N. Dinculeanu, E. Dynkin, S. Evans, N. Falkner, P. Fitzsimmons, R. Getoor, J. Glover, V. Goodman, P. Hsu, J.-F. Le Gall, M. Liao, P. March, P. McGill, J. Mitro, T. Mountford, C. Mueller, A. Mukherjea, V. Papanicolaou, E. Perkins, M. Pinsky, L. Pitt, A.O. Pittenger, Z. Pop-Stojanovic, M. Rao, J. Rosen, T. Salisbury, C. Shih, M. Taksar, J. Taylor, S.J. Taylor, E. Toby, R. Williams, Wu Rong, and Z. Zhao. The seminar was made possible through the generous support of the Department of Mathematics, the Center for Applied Mathematics, the Division of Sponsored Research and the College of Liberal Arts and Sciences of the University of Florida. We extend our thanks for local arrangements to our host, Zoran Pop-Stojanovic. 1. G.

Download or read book Semimartingales written by Michel Métivier and published by Walter de Gruyter. This book was released on 2011-06-01 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Download or read book Real and Stochastic Analysis written by M. M. Rao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 411 pages. 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.

Download or read book Probability Theory and Mathematical Statistics Vol 1 written by B. Grigelionis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "GRIGELIONIS: PROCEEDINGS OF THE FIFTH VILNIUS CONFERE E-BOOK".

Download or read book Probability Theory and Mathematical Statistics written by Bronius Grigelionis and published by VSP. This book was released on 1990 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics written by Yuri E. Gliklikh and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometrical methods in modem mathematical physics and the developments in Geometry and Global Analysis motivated by physical problems are being intensively worked out in contemporary mathematics. In particular, during the last decades a new branch of Global Analysis, Stochastic Differential Geometry, was formed to meet the needs of Mathematical Physics. It deals with a lot of various second order differential equations on finite and infinite-dimensional manifolds arising in Physics, and its validity is based on the deep inter-relation between modem Differential Geometry and certain parts of the Theory of Stochastic Processes, discovered not so long ago. The foundation of our topic is presented in the contemporary mathematical literature by a lot of publications devoted to certain parts of the above-mentioned themes and connected with the scope of material of this book. There exist some monographs on Stochastic Differential Equations on Manifolds (e. g. [9,36,38,87]) based on the Stratonovich approach. In [7] there is a detailed description of It6 equations on manifolds in Belopolskaya-Dalecky form. Nelson's book [94] deals with Stochastic Mechanics and mean derivatives on Riemannian Manifolds. The books and survey papers on the Lagrange approach to Hydrodynamics [2,31,73,88], etc. , give good presentations of the use of infinite-dimensional ordinary differential geometry in ideal hydrodynamics. We should also refer here to [89,102], to the previous books by the author [53,64], and to many others.

Download or read book Ecole d Ete de Probabilites de Saint Flour XXVIII 1998 written by M. Emery and published by Springer Science & Business Media. This book was released on 2000-06-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: MSC 2000: 46L10, 46L53