Overview
This book 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. Audience: This volume will be of interest to mathematical physicists, and mathematicians whose work involves probability theory, stochastic processes, global analysis, analysis on manifolds or differential geometry, and is recommended for graduate level courses.
Full Product Details
Author: Yuri E. Gliklikh
Publisher: Springer
Imprint: Springer
Edition: Softcover reprint of hardcover 1st ed. 1996
Volume: 374
Dimensions:
Width: 15.50cm
, Height: 1.10cm
, Length: 23.50cm
Weight: 0.454kg
ISBN: 9789048147311
ISBN 10: 904814731
Pages: 192
Publication Date: 08 December 2010
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Out of stock
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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
' ... 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
