Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1996
|
| Schriftenreihe: | Mathematics and Its Applications
374 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XVI, 192 p) |
| ISBN: | 9789401586344 9789048147311 |
| DOI: | 10.1007/978-94-015-8634-4 |
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| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401586344 9789048147311 |
| language | English |
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| spelling | Gliklikh, Yuri E. Verfasser aut Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics by Yuri E. Gliklikh Dordrecht Springer Netherlands 1996 1 Online-Ressource (XVI, 192 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 374 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 Mathematics Global analysis Global differential geometry Distribution (Probability theory) Applications of Mathematics Probability Theory and Stochastic Processes Global Analysis and Analysis on Manifolds Differential Geometry Mathematik Stochastische Differentialgeometrie (DE-588)4226826-6 gnd rswk-swf Stochastische Differentialgeometrie (DE-588)4226826-6 s 1\p DE-604 https://doi.org/10.1007/978-94-015-8634-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gliklikh, Yuri E. Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics Mathematics Global analysis Global differential geometry Distribution (Probability theory) Applications of Mathematics Probability Theory and Stochastic Processes Global Analysis and Analysis on Manifolds Differential Geometry Mathematik Stochastische Differentialgeometrie (DE-588)4226826-6 gnd |
| subject_GND | (DE-588)4226826-6 |
| title | Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics |
| title_auth | Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics |
| title_exact_search | Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics |
| title_full | Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics by Yuri E. Gliklikh |
| title_fullStr | Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics by Yuri E. Gliklikh |
| title_full_unstemmed | Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics by Yuri E. Gliklikh |
| title_short | Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics |
| title_sort | ordinary and stochastic differential geometry as a tool for mathematical physics |
| topic | Mathematics Global analysis Global differential geometry Distribution (Probability theory) Applications of Mathematics Probability Theory and Stochastic Processes Global Analysis and Analysis on Manifolds Differential Geometry Mathematik Stochastische Differentialgeometrie (DE-588)4226826-6 gnd |
| topic_facet | Mathematics Global analysis Global differential geometry Distribution (Probability theory) Applications of Mathematics Probability Theory and Stochastic Processes Global Analysis and Analysis on Manifolds Differential Geometry Mathematik Stochastische Differentialgeometrie |
| url | https://doi.org/10.1007/978-94-015-8634-4 |
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