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OverviewThis text develops new unified methods which lead to results in parts of mathematical physics traditionally considered as being far apart. The emphasis is three-fold: Firstly, this volume unifies three independently developed approaches to stochastic differential equations on manifolds, namely the theory of Ito equations in the form of Belopolskaya-Dalecky, Nelson's construction of the so-called mean derivatives of stochastic processes and the author's construction of stochastic line integrals with Riemannian parallel translation. Secondly, the book includes applications such as the Langevin equation of statistical mechanics, Nelson's stochastic mechanics (a version of quantum mechanics), and the hydrodynamics of viscous incompressible fluid treated with the modern Lagrange formalism. Considering these topics together has become possible following the discovery of their common mathematical nature. Thirdly, the work contains sufficient preliminary and background material from coordinate-free differential geometry and from the theory of stochastic differential equations to make it self-contained and convenient for mathematicians and mathematical physicists not familiar with those branches. Full Product DetailsAuthor: Yuri E. GliklikhPublisher: Springer Imprint: Springer Edition: 1996 ed. Volume: 374 Dimensions: Width: 15.60cm , Height: 1.20cm , Length: 23.40cm Weight: 1.050kg ISBN: 9780792341543ISBN 10: 0792341546 Pages: 192 Publication Date: 31 August 1996 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsI. Elements of Coordinate-Free Differential Geometry.- II. Introduction to Stochastic Analysis in Rn.- III. Stochastic Differential Equations on Manifolds.- IV. Langevin’s Equation in Geometric Form.- V. Nelson’s Stochastic Mechanics.- VI. The Lagrangian Approach to Hydrodynamics.- References.Reviews... the author has successfully arranged them [the topics] into a smooth, coherent rexposition. It is highly recommended for those readers with good background knowledge in differential geometry, stochastic analysis, and mathematical physics.' Mathematical Reviews, 98k ` ... the author has successfully arranged them [the topics] into a smooth, coherent rexposition. It is highly recommended for those readers with good background knowledge in differential geometry, stochastic analysis, and mathematical physics.' Mathematical Reviews, 98k ` ... the author has successfully arranged them [the topics] into a smooth, coherent rexposition. It is highly recommended for those readers with good background knowledge in differential geometry, stochastic analysis, and mathematical physics.' Mathematical Reviews, 98k Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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