Nonlinear Markov processes and kinetic equations:
A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in inte...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2010
|
| Series: | Cambridge tracts in mathematics
182 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology |
| Physical Description: | 1 Online-Ressource (xvii, 375 Seiten) |
| ISBN: | 9780511760303 |
| DOI: | 10.1017/CBO9780511760303 |
Staff View
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| 520 | |a A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology | ||
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| author | Kolokolʹcov, Vassilij N. 1959- |
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| contents | Introduction -- Tools from Markov process theory -- Nonlinear Markov processes and semigroups -- Applications to interating particles |
| ctrlnum | (ZDB-20-CBO)CR9780511760303 (OCoLC)852520031 (DE-599)BVBBV043942006 |
| dewey-full | 519.233 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| id | DE-604.BV043942006 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511760303 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350976 |
| oclc_num | 852520031 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xvii, 375 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Kolokolʹcov, Vassilij N. 1959- Verfasser (DE-588)121728633 aut Nonlinear Markov processes and kinetic equations Vassili N. Kolokoltsov Nonlinear Markov Processes & Kinetic Equations Cambridge Cambridge University Press 2010 1 Online-Ressource (xvii, 375 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 182 Introduction -- Tools from Markov process theory -- Nonlinear Markov processes and semigroups -- Applications to interating particles A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology Markov processes Nonlinear theories Kinetic theory of matter Kinetische Gleichung (DE-588)4030667-7 gnd rswk-swf Nichtlinearer Prozess (DE-588)4304582-0 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s Nichtlinearer Prozess (DE-588)4304582-0 s Kinetische Gleichung (DE-588)4030667-7 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-11184-3 https://doi.org/10.1017/CBO9780511760303 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kolokolʹcov, Vassilij N. 1959- Nonlinear Markov processes and kinetic equations Introduction -- Tools from Markov process theory -- Nonlinear Markov processes and semigroups -- Applications to interating particles Markov processes Nonlinear theories Kinetic theory of matter Kinetische Gleichung (DE-588)4030667-7 gnd Nichtlinearer Prozess (DE-588)4304582-0 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| subject_GND | (DE-588)4030667-7 (DE-588)4304582-0 (DE-588)4134948-9 |
| title | Nonlinear Markov processes and kinetic equations |
| title_alt | Nonlinear Markov Processes & Kinetic Equations |
| title_auth | Nonlinear Markov processes and kinetic equations |
| title_exact_search | Nonlinear Markov processes and kinetic equations |
| title_full | Nonlinear Markov processes and kinetic equations Vassili N. Kolokoltsov |
| title_fullStr | Nonlinear Markov processes and kinetic equations Vassili N. Kolokoltsov |
| title_full_unstemmed | Nonlinear Markov processes and kinetic equations Vassili N. Kolokoltsov |
| title_short | Nonlinear Markov processes and kinetic equations |
| title_sort | nonlinear markov processes and kinetic equations |
| topic | Markov processes Nonlinear theories Kinetic theory of matter Kinetische Gleichung (DE-588)4030667-7 gnd Nichtlinearer Prozess (DE-588)4304582-0 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| topic_facet | Markov processes Nonlinear theories Kinetic theory of matter Kinetische Gleichung Nichtlinearer Prozess Markov-Prozess |
| url | https://doi.org/10.1017/CBO9780511760303 |
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