书目名称 | Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics | 编辑 | Yuri E. Gliklikh | 视频video | | 丛书名称 | Mathematics and Its Applications | 图书封面 |  | 描述 | 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 Riema | 出版日期 | Book 1996 | 关键词 | Probability theory; Stochastic processes; differential geometry; manifold; mathematical physics; stochast | 版次 | 1 | doi | https://doi.org/10.1007/978-94-015-8634-4 | isbn_softcover | 978-90-481-4731-1 | isbn_ebook | 978-94-015-8634-4 | copyright | Springer Science+Business Media Dordrecht 1996 |
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