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...
The geometrical methods in modem mathematical physics and the developments in Geometry and Global Analysis motivated by physical problems are being in...
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...
This book develops new unified methods which lead to results in parts of mathematical physics traditionally considered as being far apart. The emphasi...
The main aim of this book is to develop the methods of Global Analysis and of 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 quite distant from each other and requiring different methods of investigation. Among those areas we mention classical mechanics on non-linear configuration spaces, some problems of statistical and quantum physics, hydrodynamics, etc. The idea, yielding the unification of these topics, is based on the use of a geometrically invariant form of...
The main aim of this book is to develop the methods of Global Analysis and of Stochastic Analysis such that their combination allows one to have a ...
The main aim of this book is to develop the methods of Global Analysis and of 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 quite distant from each other and requiring different methods of investigation. Among those areas we mention classical mechanics on non-linear configuration spaces, some problems of statistical and quantum physics, hydrodynamics, etc. The idea, yielding the unification of these topics, is based on the use of a geometrically invariant form of...
The main aim of this book is to develop the methods of Global Analysis and of Stochastic Analysis such that their combination allows one to have a ...
