Global And Stochastic Analysis With Applications To Mathematical Physics
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Global and Stochastic Analysis with Applications to Mathematical Physics
Author: Yuri E. Gliklikh
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-12-07
Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems. This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation. Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics. A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.
Nonstandard Methods in Stochastic Analysis and Mathematical Physics
Author: Sergio Albeverio
language: en
Publisher: Courier Dover Publications
Release Date: 2009-02-26
Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." — Bulletin of the American Mathematical Society. 1986 edition.
Stochastic Analysis on Manifolds
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.