[PDF] Stochastic Differential Equations On Manifolds eBook

Author : K. D. Elworthy
Publisher : Cambridge University Press
Page : 347 pages
File Size : 32,98 MB
Release : 1982
Category : Manifolds (Mathematics).
ISBN : 0521287677

GET BOOK

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.

Author : Michel Emery
Publisher : Springer Science & Business Media
Page : 158 pages
File Size : 43,94 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642750516

GET BOOK

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.

Author : Mickaël D. Chekroun
Publisher : Springer
Page : 141 pages
File Size : 14,38 MB
Release : 2014-12-23
Category : Mathematics
ISBN : 3319125206

GET BOOK

In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.

Author : Elton P. Hsu
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 25,80 MB
Release : 2002
Category : Mathematics
ISBN : 0821808028

GET BOOK

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.

Author : Fabrice Blache
Publisher : Omniscriptum
Page : 148 pages
File Size : 14,46 MB
Release : 2018-02-28
Category :
ISBN : 9786131536854

GET BOOK

This thesis is devoted to the study of some kind of Backward Stochastic Differential Equations (BSDE for short) with a drift f, whose solutions belong to a Riemannian manifold with connection. It generalizes two well-known problems: the research for martingales with prescribed terminal value, and the existence and uniqueness of solutions to euclidean BSDE with Lipschitz drift, originally studied by E. Pardoux and S. Peng.

Author : Ya.I. Belopolskaya
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 21,36 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 9400922159

GET BOOK

'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.

Author : L. Accardi
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 25,61 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461222249

GET BOOK

Senior probabilists from around the world with widely differing specialities gave their visions of the state of their specialty, why they think it is important, and how they think it will develop in the new millenium. The volume includes papers given at a symposium at Columbia University in 1995, but papers from others not at the meeting were added to broaden the coverage of areas. All papers were refereed.

Author : Simo Särkkä
Publisher : Cambridge University Press
Page : 327 pages
File Size : 33,47 MB
Release : 2019-05-02
Category : Business & Economics
ISBN : 1316510085

GET BOOK

With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Author : Hiroshi Kunita
Publisher : Cambridge University Press
Page : 364 pages
File Size : 26,37 MB
Release : 1990
Category : Mathematics
ISBN : 9780521599252

GET BOOK

The main purpose of this book is to give a systematic treatment of the theory of stochastic differential equations and stochastic flow of diffeomorphisms, and through the former to study the properties of stochastic flows.The classical theory was initiated by K. Itô and since then has been much developed. Professor Kunita's approach here is to regard the stochastic differential equation as a dynamical system driven by a random vector field, including thereby Itô's theory as a special case. The book can be used with advanced courses on probability theory or for self-study.