Random Perturbations of Dynamical Systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1988
|
| Schriftenreihe: | Progress in Probability and Statistics
16 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Mathematicians often face the question to which extent mathematical models describe processes of the real world. These models are derived from experimental data, hence they describe real phenomena only approximately. Thus a mathematical approach must begin with choosing properties which are not very sensitive to small changes in the model, and so may be viewed as properties of the real process. In particular, this concerns real processes which can be described by means of ordinary differential equations. By this reason different notions of stability played an important role in the qualitative theory of ordinary differential equations commonly known nowdays as the theory of dynamical systems. Since physical processes are usually affected by an enormous number of small external fluctuations whose resulting action would be natural to consider as random, the stability of dynamical systems with respect to random perturbations comes into the picture. There are differences between the study of stability properties of single trajectories, i. e. , the Lyapunov stability, and the global stability of dynamical systems. The stochastic Lyapunov stability was dealt with in Hasminskii [Has]. In this book we are concerned mainly with questions of global stability in the presence of noise which can be described as recovering parameters of dynamical systems from the study of their random perturbations. The parameters which is possible to obtain in this way can be considered as stable under random perturbations, and so having physical sense. -1- Our set up is the following |
| Beschreibung: | 1 Online-Ressource (VIII, 294p) |
| ISBN: | 9781461581819 9781461581833 |
| DOI: | 10.1007/978-1-4615-8181-9 |
Internformat
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| 500 | |a Mathematicians often face the question to which extent mathematical models describe processes of the real world. These models are derived from experimental data, hence they describe real phenomena only approximately. Thus a mathematical approach must begin with choosing properties which are not very sensitive to small changes in the model, and so may be viewed as properties of the real process. In particular, this concerns real processes which can be described by means of ordinary differential equations. By this reason different notions of stability played an important role in the qualitative theory of ordinary differential equations commonly known nowdays as the theory of dynamical systems. Since physical processes are usually affected by an enormous number of small external fluctuations whose resulting action would be natural to consider as random, the stability of dynamical systems with respect to random perturbations comes into the picture. There are differences between the study of stability properties of single trajectories, i. e. , the Lyapunov stability, and the global stability of dynamical systems. The stochastic Lyapunov stability was dealt with in Hasminskii [Has]. In this book we are concerned mainly with questions of global stability in the presence of noise which can be described as recovering parameters of dynamical systems from the study of their random perturbations. The parameters which is possible to obtain in this way can be considered as stable under random perturbations, and so having physical sense. -1- Our set up is the following | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Kifer, Yuri |
| author_facet | Kifer, Yuri |
| author_role | aut |
| author_sort | Kifer, Yuri |
| author_variant | y k yk |
| building | Verbundindex |
| bvnumber | BV042420960 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik |
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| format | Electronic eBook |
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| id | DE-604.BV042420960 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781461581819 9781461581833 |
| language | English |
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| publishDate | 1988 |
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| publisher | Birkhäuser Boston |
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| series2 | Progress in Probability and Statistics |
| spelling | Kifer, Yuri Verfasser aut Random Perturbations of Dynamical Systems by Yuri Kifer Boston, MA Birkhäuser Boston 1988 1 Online-Ressource (VIII, 294p) txt rdacontent c rdamedia cr rdacarrier Progress in Probability and Statistics 16 Mathematicians often face the question to which extent mathematical models describe processes of the real world. These models are derived from experimental data, hence they describe real phenomena only approximately. Thus a mathematical approach must begin with choosing properties which are not very sensitive to small changes in the model, and so may be viewed as properties of the real process. In particular, this concerns real processes which can be described by means of ordinary differential equations. By this reason different notions of stability played an important role in the qualitative theory of ordinary differential equations commonly known nowdays as the theory of dynamical systems. Since physical processes are usually affected by an enormous number of small external fluctuations whose resulting action would be natural to consider as random, the stability of dynamical systems with respect to random perturbations comes into the picture. There are differences between the study of stability properties of single trajectories, i. e. , the Lyapunov stability, and the global stability of dynamical systems. The stochastic Lyapunov stability was dealt with in Hasminskii [Has]. In this book we are concerned mainly with questions of global stability in the presence of noise which can be described as recovering parameters of dynamical systems from the study of their random perturbations. The parameters which is possible to obtain in this way can be considered as stable under random perturbations, and so having physical sense. -1- Our set up is the following Mathematics Differentiable dynamical systems Differential equations, partial Distribution (Probability theory) Mathematical physics Probability Theory and Stochastic Processes Mathematical Methods in Physics Dynamical Systems and Ergodic Theory Statistical Physics, Dynamical Systems and Complexity Classical Continuum Physics Partial Differential Equations Mathematik Mathematische Physik Störungstheorie (DE-588)4128420-3 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Dynamisches System (DE-588)4013396-5 s 1\p DE-604 Störungstheorie (DE-588)4128420-3 s 2\p DE-604 https://doi.org/10.1007/978-1-4615-8181-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kifer, Yuri Random Perturbations of Dynamical Systems Mathematics Differentiable dynamical systems Differential equations, partial Distribution (Probability theory) Mathematical physics Probability Theory and Stochastic Processes Mathematical Methods in Physics Dynamical Systems and Ergodic Theory Statistical Physics, Dynamical Systems and Complexity Classical Continuum Physics Partial Differential Equations Mathematik Mathematische Physik Störungstheorie (DE-588)4128420-3 gnd Dynamisches System (DE-588)4013396-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4128420-3 (DE-588)4013396-5 (DE-588)4057630-9 |
| title | Random Perturbations of Dynamical Systems |
| title_auth | Random Perturbations of Dynamical Systems |
| title_exact_search | Random Perturbations of Dynamical Systems |
| title_full | Random Perturbations of Dynamical Systems by Yuri Kifer |
| title_fullStr | Random Perturbations of Dynamical Systems by Yuri Kifer |
| title_full_unstemmed | Random Perturbations of Dynamical Systems by Yuri Kifer |
| title_short | Random Perturbations of Dynamical Systems |
| title_sort | random perturbations of dynamical systems |
| topic | Mathematics Differentiable dynamical systems Differential equations, partial Distribution (Probability theory) Mathematical physics Probability Theory and Stochastic Processes Mathematical Methods in Physics Dynamical Systems and Ergodic Theory Statistical Physics, Dynamical Systems and Complexity Classical Continuum Physics Partial Differential Equations Mathematik Mathematische Physik Störungstheorie (DE-588)4128420-3 gnd Dynamisches System (DE-588)4013396-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Mathematics Differentiable dynamical systems Differential equations, partial Distribution (Probability theory) Mathematical physics Probability Theory and Stochastic Processes Mathematical Methods in Physics Dynamical Systems and Ergodic Theory Statistical Physics, Dynamical Systems and Complexity Classical Continuum Physics Partial Differential Equations Mathematik Mathematische Physik Störungstheorie Dynamisches System Stochastischer Prozess |
| url | https://doi.org/10.1007/978-1-4615-8181-9 |
| work_keys_str_mv | AT kiferyuri randomperturbationsofdynamicalsystems |