Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics

By:

Yuri E. Gliklikh

Format:

Hardback

Series:

Mathematics and its Applications

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Description

This 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.

Release date NZ

August 31st, 1996

Author

Yuri E. Gliklikh

Audience

Professional & Vocational

Illustrations

XVI, 192 p.

Pages

192

Series

Mathematics and its Applications

Dimensions

156x234x12

ISBN-13

9780792341543

Product ID

2437397

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