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Stochastic Analysis on Manifolds

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 028/5 ( reviews)

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Book Synopsis Stochastic Analysis on Manifolds by : Elton P. Hsu

Download or read book Stochastic Analysis on Manifolds written by Elton P. Hsu. This book was released on 2002. 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.

Stochastic Calculus in Manifolds

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 516/5 ( reviews)

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Book Synopsis Stochastic Calculus in Manifolds by : Michel Emery

Download or read book Stochastic Calculus in Manifolds written by Michel Emery. This book was released on 2012-12-06. 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.

Stochastic Differential Equations on Manifolds

1982 Manifolds (Mathematics).
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Release : 1982
Genre : Manifolds (Mathematics).
Kind : eBook
Book Rating : 677/5 ( reviews)

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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. This book was released on 1982. 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.

An Introduction to the Analysis of Paths on a Riemannian Manifold

2000 Mathematics
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Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 393/5 ( reviews)

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Book Synopsis An Introduction to the Analysis of Paths on a Riemannian Manifold by : Daniel W. Stroock

Download or read book An Introduction to the Analysis of Paths on a Riemannian Manifold written by Daniel W. Stroock. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.

Stochastic Equations and Differential Geometry

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 159/5 ( reviews)

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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. This book was released on 2012-12-06. 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.

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