Random Evolutions and Their Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | Mathematics and Its Applications
408 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The main purpose of this handbook is to summarize and to put in order the ideas, methods, results and literature on the theory of random evolutions and their applications to the evolutionary stochastic systems in random media, and also to present some new trends in the theory of random evolutions and their applications. In physical language, a random evolution ( RE ) is a model for a dynamical sys tem whose state of evolution is subject to random variations. Such systems arise in all branches of science. For example, random Hamiltonian and Schrodinger equations with random potential in quantum mechanics, Maxwell's equation with a random refractive index in electrodynamics, transport equations associated with the trajec tory of a particle whose speed and direction change at random, etc. There are the examples of a single abstract situation in which an evolving system changes its "mode of evolution" or "law of motion" because of random changes of the "environment" or in a "medium". So, in mathematical language, a RE is a solution of stochastic operator integral equations in a Banach space. The operator coefficients of such equations depend on random parameters. Of course, in such generality , our equation includes any homogeneous linear evolving system. Particular examples of such equations were studied in physical applications many years ago. A general mathematical theory of such equations has been developed since 1969, the Theory of Random Evolutions |
| Beschreibung: | 1 Online-Ressource (XVI, 183 p) |
| ISBN: | 9789401157544 9789401064279 |
| DOI: | 10.1007/978-94-011-5754-4 |
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| isbn | 9789401157544 9789401064279 |
| language | English |
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| spelling | Swishchuk, Anatoly Verfasser aut Random Evolutions and Their Applications by Anatoly Swishchuk Dordrecht Springer Netherlands 1997 1 Online-Ressource (XVI, 183 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 408 The main purpose of this handbook is to summarize and to put in order the ideas, methods, results and literature on the theory of random evolutions and their applications to the evolutionary stochastic systems in random media, and also to present some new trends in the theory of random evolutions and their applications. In physical language, a random evolution ( RE ) is a model for a dynamical sys tem whose state of evolution is subject to random variations. Such systems arise in all branches of science. For example, random Hamiltonian and Schrodinger equations with random potential in quantum mechanics, Maxwell's equation with a random refractive index in electrodynamics, transport equations associated with the trajec tory of a particle whose speed and direction change at random, etc. There are the examples of a single abstract situation in which an evolving system changes its "mode of evolution" or "law of motion" because of random changes of the "environment" or in a "medium". So, in mathematical language, a RE is a solution of stochastic operator integral equations in a Banach space. The operator coefficients of such equations depend on random parameters. Of course, in such generality , our equation includes any homogeneous linear evolving system. Particular examples of such equations were studied in physical applications many years ago. A general mathematical theory of such equations has been developed since 1969, the Theory of Random Evolutions Mathematics Functional analysis Operator theory Mathematical optimization Distribution (Probability theory) Economics / Statistics Probability Theory and Stochastic Processes Functional Analysis Operator Theory Calculus of Variations and Optimal Control; Optimization Statistics for Business/Economics/Mathematical Finance/Insurance Mathematik Statistik Wirtschaft Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s 1\p DE-604 https://doi.org/10.1007/978-94-011-5754-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Swishchuk, Anatoly Random Evolutions and Their Applications Mathematics Functional analysis Operator theory Mathematical optimization Distribution (Probability theory) Economics / Statistics Probability Theory and Stochastic Processes Functional Analysis Operator Theory Calculus of Variations and Optimal Control; Optimization Statistics for Business/Economics/Mathematical Finance/Insurance Mathematik Statistik Wirtschaft Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Random Evolutions and Their Applications |
| title_auth | Random Evolutions and Their Applications |
| title_exact_search | Random Evolutions and Their Applications |
| title_full | Random Evolutions and Their Applications by Anatoly Swishchuk |
| title_fullStr | Random Evolutions and Their Applications by Anatoly Swishchuk |
| title_full_unstemmed | Random Evolutions and Their Applications by Anatoly Swishchuk |
| title_short | Random Evolutions and Their Applications |
| title_sort | random evolutions and their applications |
| topic | Mathematics Functional analysis Operator theory Mathematical optimization Distribution (Probability theory) Economics / Statistics Probability Theory and Stochastic Processes Functional Analysis Operator Theory Calculus of Variations and Optimal Control; Optimization Statistics for Business/Economics/Mathematical Finance/Insurance Mathematik Statistik Wirtschaft Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Mathematics Functional analysis Operator theory Mathematical optimization Distribution (Probability theory) Economics / Statistics Probability Theory and Stochastic Processes Functional Analysis Operator Theory Calculus of Variations and Optimal Control; Optimization Statistics for Business/Economics/Mathematical Finance/Insurance Mathematik Statistik Wirtschaft Stochastischer Prozess |
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