Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics write by Yuri E. Gliklikh. This book was released on 2013-03-14. Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics available in PDF, EPUB and Kindle. The geometrical methods in modem mathematical physics and the developments in Geometry and Global Analysis motivated by physical problems are being intensively worked out in contemporary mathematics. In particular, during the last decades a new branch of Global Analysis, Stochastic Differential Geometry, was formed to meet the needs of Mathematical Physics. It deals with a lot of various second order differential equations on finite and infinite-dimensional manifolds arising in Physics, and its validity is based on the deep inter-relation between modem Differential Geometry and certain parts of the Theory of Stochastic Processes, discovered not so long ago. The foundation of our topic is presented in the contemporary mathematical literature by a lot of publications devoted to certain parts of the above-mentioned themes and connected with the scope of material of this book. There exist some monographs on Stochastic Differential Equations on Manifolds (e. g. [9,36,38,87]) based on the Stratonovich approach. In [7] there is a detailed description of It6 equations on manifolds in Belopolskaya-Dalecky form. Nelson's book [94] deals with Stochastic Mechanics and mean derivatives on Riemannian Manifolds. The books and survey papers on the Lagrange approach to Hydrodynamics [2,31,73,88], etc. , give good presentations of the use of infinite-dimensional ordinary differential geometry in ideal hydrodynamics. We should also refer here to [89,102], to the previous books by the author [53,64], and to many others.
Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics
Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics write by Yuri E. Gliklikh. This book was released on 1996-08-31. Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics available in PDF, EPUB and Kindle. The geometrical methods in modem mathematical physics and the developments in Geometry and Global Analysis motivated by physical problems are being intensively worked out in contemporary mathematics. In particular, during the last decades a new branch of Global Analysis, Stochastic Differential Geometry, was formed to meet the needs of Mathematical Physics. It deals with a lot of various second order differential equations on finite and infinite-dimensional manifolds arising in Physics, and its validity is based on the deep inter-relation between modem Differential Geometry and certain parts of the Theory of Stochastic Processes, discovered not so long ago. The foundation of our topic is presented in the contemporary mathematical literature by a lot of publications devoted to certain parts of the above-mentioned themes and connected with the scope of material of this book. There exist some monographs on Stochastic Differential Equations on Manifolds (e. g. [9,36,38,87]) based on the Stratonovich approach. In [7] there is a detailed description of It6 equations on manifolds in Belopolskaya-Dalecky form. Nelson's book [94] deals with Stochastic Mechanics and mean derivatives on Riemannian Manifolds. The books and survey papers on the Lagrange approach to Hydrodynamics [2,31,73,88], etc. , give good presentations of the use of infinite-dimensional ordinary differential geometry in ideal hydrodynamics. We should also refer here to [89,102], to the previous books by the author [53,64], and to many others.
Stochastic Equations and Differential Geometry
Stochastic Equations and Differential Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Equations and Differential Geometry write by Ya.I. Belopolskaya. This book was released on 2012-12-06. Stochastic Equations and Differential Geometry available in PDF, EPUB and Kindle. '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.
Global Analysis in Mathematical Physics
Global Analysis in Mathematical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Global Analysis in Mathematical Physics write by I︠U︡. E. Gliklikh. This book was released on 1997. Global Analysis in Mathematical Physics available in PDF, EPUB and Kindle. This book is the first in monographic literature giving a common treatment to three areas of applications of Global Analysis in Mathematical Physics previously considered quite distant from each other, namely, differential geometry applied to classical mechanics, stochastic differential geometry used in quantum and statistical mechanics, and infinite-dimensional differential geometry fundamental for hydrodynamics. The unification of these topics is made possible by considering the Newton equation or its natural generalizations and analogues as a fundamental equation of motion. New general geometric and stochastic methods of investigation are developed, and new results on existence, uniqueness, and qualitative behavior of solutions are obtained.
New Trends in Stochastic Analysis and Related Topics
New Trends in Stochastic Analysis and Related Topics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook New Trends in Stochastic Analysis and Related Topics write by Huaizhong Zhao. This book was released on 2012. New Trends in Stochastic Analysis and Related Topics available in PDF, EPUB and Kindle. The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.
