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Stochastic Equations And Differential Geometry
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Book Synopsis Stochastic Equations and Differential Geometry by : Ya.I. Belopolskaya
Download or read book Stochastic Equations and Differential Geometry written by Ya.I. Belopolskaya and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Book Synopsis Stochastic Differential Equations on Manifolds by : K. D. Elworthy
Download or read book Stochastic Differential Equations on Manifolds written by K. D. Elworthy and published by Cambridge University Press. This book was released on 1982 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aims of this book, originally published in 1982, are to give an understanding of the basic ideas concerning stochastic differential equations on manifolds and their solution flows, to examine the properties of Brownian motion on Riemannian manifolds when it is constructed using the stochiastic development and to indicate some of the uses of the theory. The author has included two appendices which summarise the manifold theory and differential geometry needed to follow the development; coordinate-free notation is used throughout. Moreover, the stochiastic integrals used are those which can be obtained from limits of the Riemann sums, thereby avoiding much of the technicalities of the general theory of processes and allowing the reader to get a quick grasp of the fundamental ideas of stochastic integration as they are needed for a variety of applications.
Book Synopsis Stochastic Differential Equations by : Bernt Oksendal
Download or read book Stochastic Differential Equations written by Bernt Oksendal and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.
Book Synopsis Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics by : Yuri E. Gliklikh
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.
Book Synopsis Stochastic Calculus in Manifolds by : Michel Emery
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.
Book Synopsis Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics by : Yuri E. Gliklikh
Download or read book Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics written by Yuri E. Gliklikh and published by Springer. This book was released on 1996-08-31 with total page 192 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.
Book Synopsis Stochastic Differential Geometry at Saint-Flour by : Alano Ancona
Download or read book Stochastic Differential Geometry at Saint-Flour written by Alano Ancona and published by Springer. This book was released on 2012-12-22 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kunita, H.:Stochastic differential equations and stochastic flows of diffeomorphisms.-Elworthy, D.: Geometric aspects of diffusions on manifolds.-Ancona, A.:Théorie du potential sur les graphs et les variétiés.-Emery, M.:Continuous martingales in differentiable manifolds.
Book Synopsis An Introduction to the Geometry of Stochastic Flows by : Fabrice Baudoin
Download or read book An Introduction to the Geometry of Stochastic Flows written by Fabrice Baudoin and published by World Scientific. This book was released on 2004 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide a self-contained introduction to the local geometry of the stochastic flows associated with stochastic differential equations. It stresses the view that the local geometry of any stochastic flow is determined very precisely and explicitly by a universal formula referred to as the Chen-Strichartz formula. The natural geometry associated with the Chen-Strichartz formula is the sub-Riemannian geometry whose main tools are introduced throughout the text. By using the connection between stochastic flows and partial differential equations, we apply this point of view of the study of hypoelliptic operators written in Hormander's form.
Book Synopsis Stochastic Analysis on Manifolds by : Elton P. Hsu
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: Concerned with probability theory, Elton Hsu's study focuses primarily on the relations between Brownian motion on a manifold and analytical aspects of differential geometry. A key theme is the probabilistic interpretation of the curvature of a manifold
Book Synopsis Stochastic Calculus and Differential Equations for Physics and Finance by : Joseph L. McCauley
Download or read book Stochastic Calculus and Differential Equations for Physics and Finance written by Joseph L. McCauley and published by Cambridge University Press. This book was released on 2013-02-21 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides graduate students and practitioners in physics and economics with a better understanding of stochastic processes.
Book Synopsis Stochastic and Integral Geometry by : R.V. Ambartzumian
Download or read book Stochastic and Integral Geometry written by R.V. Ambartzumian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Analysis and Nonlinear Partial Differential Equations by : Stefan Hildebrandt
Download or read book Geometric Analysis and Nonlinear Partial Differential Equations written by Stefan Hildebrandt and published by Springer Science & Business Media. This book was released on 2003 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-organized and coherent collection of papers leads the reader to the frontiers of present research in the theory of nonlinear partial differential equations and the calculus of variations and offers insight into some exciting developments. In addition, most articles also provide an excellent introduction to their background, describing extensively as they do the history of those problems presented, as well as the state of the art and offer a well-chosen guide to the literature. Part I contains the contributions of geometric nature: From spectral theory on regular and singular spaces to regularity theory of solutions of variational problems. Part II consists of articles on partial differential equations which originate from problems in physics, biology and stochastics. They cover elliptic, hyperbolic and parabolic cases.
Book Synopsis Stochastic Partial Differential Equations by : Sergey V. Lototsky
Download or read book Stochastic Partial Differential Equations written by Sergey V. Lototsky and published by Springer. This book was released on 2017-07-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for time, can move on. Accordingly, no solutions are provided, but there are often hints on how to proceed. The book will be of interest to everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field.
Book Synopsis On the Geometry of Diffusion Operators and Stochastic Flows by : K.D. Elworthy
Download or read book On the Geometry of Diffusion Operators and Stochastic Flows written by K.D. Elworthy and published by Springer. This book was released on 2007-01-05 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters.
Book Synopsis Global Analysis in Mathematical Physics by : I︠U︡. E. Gliklikh
Download or read book Global Analysis in Mathematical Physics written by I︠U︡. E. Gliklikh and published by Springer Science & Business Media. This book was released on 1997 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first in monographic literature giving a common treatment to three areas of applications of Global Analysis in Mathematical Physics previously considered quite distant from each other, namely, differential geometry applied to classical mechanics, stochastic differential geometry used in quantum and statistical mechanics, and infinite-dimensional differential geometry fundamental for hydrodynamics. The unification of these topics is made possible by considering the Newton equation or its natural generalizations and analogues as a fundamental equation of motion. New general geometric and stochastic methods of investigation are developed, and new results on existence, uniqueness, and qualitative behavior of solutions are obtained.
Book Synopsis Stochastic Differential Equations by : Peter H. Baxendale
Download or read book Stochastic Differential Equations written by Peter H. Baxendale and published by World Scientific. This book was released on 2007 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract attention of mathematicians of all generations, because, together with a short but thorough introduction to SPDEs, it presents a number of optimal and essentially non-improvable results about solvability for a large class of both linear and non-linear equations.
Book Synopsis Differential Geometry and Its Applications by : John Oprea
Download or read book Differential Geometry and Its Applications written by John Oprea and published by MAA. This book was released on 2007-09-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the differential geometry of surfaces and its relevance to engineering and the sciences.
