Interacting multiagent systems: kinetic equations and Monte Carlo methods
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2014
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 376 S. Ill., graph. Darst. |
| ISBN: | 9780199655465 |
Internformat
MARC
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| 245 | 1 | 0 | |a Interacting multiagent systems |b kinetic equations and Monte Carlo methods |c Lorenzo Pareschi ; Giuseppe Toscani |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2014 | |
| 300 | |a XIV, 376 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804151740472229888 |
|---|---|
| adam_text | Titel: Interacting multiagent systems
Autor: Pareschi, Lorenzo
Jahr: 2014
Contents
PART I KINETIC MODELLING AND SIMULATION
A short introduction to kinetic equations 3
1.1 Boltzmann s legacy 3
1.2 Notation 8
1.3 Some linear kinetic modeis 11
1.4 Binary interaction modeis on the real line 26
1.5 Binary interaction modeis on the half-line 36
1.6 Some classical results 40
Mathematical tools 48
2.1 How to be certain of the predictions of a model? 48
2.2 Some mathematical tools 49
2.3 The drift equation and Dirac delta functions 57
2.4 Dissipative modeis and the drift equation 61
2.5 Growth processes 69
Monte Carlo strategies 79
3.1 Why Monte Carlo methods? 79
3.2 Generating random variables 83
3.3 Monte Carlo techniques 96
3.4 Applications to evolutionary PDEs 110
Monte Carlo methods for kinetic equations 123
4.1 The general framework 123
4.2 Relaxation problems 125
4.3 Binary interaction modeis 131
4.4 Asymptotic preserving Monte Carlo 139
4.5 Kinetic approximation of diffusion equations 143
4.6 Remarks on multi-dimensional problems 149
PART II MULTIAGENT KINETIC EQUATIONS
Models for wealth distribution 159
5.1 Wealth, trades and kinetic equations 159
5.2 Economic and kinetic dictionaries 162
5.3 Kinetic market modeis for conservative economies 165
5.4 Non-conservative kinetic market modeis 181
5.5 Exact Solutions 189
5.6 Modelling heterogeneous traders 199
5.7 Individual preferences 205
xiv Contents
5.8 Taxation and wealth redistribution 210
6 Opinion modelling and consensus formation 225
6.1 Opinion formation 225
6.2 Kinetic modeis of opinion formation 227
6.3 Other Fokker-Planck modeis of opinion formation 238
6.4 Choice formation and influence of external factors 244
6.5 Opinion formation in the presence of leaders 252
7 A further insight into economics and social sciences 259
7.1 Towards more realistic modeis 259
7.2 A kinetic model for trading goods 261
7.3 Modelling speculative financial markets 272
7.4 A model for different groups of traders 281
7.5 Inhomogeneous modeis for the evolution of wealth 295
8 Modelling in life sciences 308
8.1 The Luria-Delbrück distribution 308
8.2 The quasi-invariant limit of the growth of mutant cells 315
8.3 Self-organized Systems and swarming modeis 322
8.4 Systems interacting with few individuals 335
8.5 Final remarks 340
Appendix A Basic arguments on Fourier transforms 341
A.l Definitions 341
A.2 Properties of the Fourier transform 342
Appendix B Important probability distributions 346
B.l Uniform distribution 346
B.2 Beta distribution 346
B.3 Normal distribution 347
B.4 Exponential distribution 347
B.5 Gamma distribution 348
B.6 Bernoulli distribution 348
B.7 Poisson distribution 349
List of figures 350
References 356
Index 374
|
| any_adam_object | 1 |
| author | Pareschi, Lorenzo 1966- Toscani, Giuseppe |
| author_GND | (DE-588)1048206947 |
| author_facet | Pareschi, Lorenzo 1966- Toscani, Giuseppe |
| author_role | aut aut |
| author_sort | Pareschi, Lorenzo 1966- |
| author_variant | l p lp g t gt |
| building | Verbundindex |
| bvnumber | BV041556837 |
| classification_rvk | SK 820 SK 990 |
| classification_tum | MSR 590f MAT 021f |
| ctrlnum | (OCoLC)869872113 (DE-599)BSZ395091969 |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV041556837 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:59:37Z |
| institution | BVB |
| isbn | 9780199655465 |
| language | English |
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| physical | XIV, 376 S. Ill., graph. Darst. |
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| publisher | Oxford Univ. Press |
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| spelling | Pareschi, Lorenzo 1966- Verfasser (DE-588)1048206947 aut Interacting multiagent systems kinetic equations and Monte Carlo methods Lorenzo Pareschi ; Giuseppe Toscani 1. ed. Oxford Oxford Univ. Press 2014 XIV, 376 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Kinetische Gleichung (DE-588)4030667-7 gnd rswk-swf Meinungsbildung (DE-588)4038461-5 gnd rswk-swf Mehragentensystem (DE-588)4389058-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Komplexes System (DE-588)4114261-5 gnd rswk-swf Schwarmverhalten (DE-588)4180330-9 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Kollektives Verhalten (DE-588)4130047-6 gnd rswk-swf Vermögensverteilung (DE-588)4063086-9 gnd rswk-swf Mehragentensystem (DE-588)4389058-1 s Kinetische Gleichung (DE-588)4030667-7 s Monte-Carlo-Simulation (DE-588)4240945-7 s Mathematische Modellierung (DE-588)7651795-0 s Vermögensverteilung (DE-588)4063086-9 s Meinungsbildung (DE-588)4038461-5 s Schwarmverhalten (DE-588)4180330-9 s Kollektives Verhalten (DE-588)4130047-6 s DE-604 Komplexes System (DE-588)4114261-5 s Mathematisches Modell (DE-588)4114528-8 s Toscani, Giuseppe Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027002439&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pareschi, Lorenzo 1966- Toscani, Giuseppe Interacting multiagent systems kinetic equations and Monte Carlo methods Monte-Carlo-Simulation (DE-588)4240945-7 gnd Kinetische Gleichung (DE-588)4030667-7 gnd Meinungsbildung (DE-588)4038461-5 gnd Mehragentensystem (DE-588)4389058-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Komplexes System (DE-588)4114261-5 gnd Schwarmverhalten (DE-588)4180330-9 gnd Mathematische Modellierung (DE-588)7651795-0 gnd Kollektives Verhalten (DE-588)4130047-6 gnd Vermögensverteilung (DE-588)4063086-9 gnd |
| subject_GND | (DE-588)4240945-7 (DE-588)4030667-7 (DE-588)4038461-5 (DE-588)4389058-1 (DE-588)4114528-8 (DE-588)4114261-5 (DE-588)4180330-9 (DE-588)7651795-0 (DE-588)4130047-6 (DE-588)4063086-9 |
| title | Interacting multiagent systems kinetic equations and Monte Carlo methods |
| title_auth | Interacting multiagent systems kinetic equations and Monte Carlo methods |
| title_exact_search | Interacting multiagent systems kinetic equations and Monte Carlo methods |
| title_full | Interacting multiagent systems kinetic equations and Monte Carlo methods Lorenzo Pareschi ; Giuseppe Toscani |
| title_fullStr | Interacting multiagent systems kinetic equations and Monte Carlo methods Lorenzo Pareschi ; Giuseppe Toscani |
| title_full_unstemmed | Interacting multiagent systems kinetic equations and Monte Carlo methods Lorenzo Pareschi ; Giuseppe Toscani |
| title_short | Interacting multiagent systems |
| title_sort | interacting multiagent systems kinetic equations and monte carlo methods |
| title_sub | kinetic equations and Monte Carlo methods |
| topic | Monte-Carlo-Simulation (DE-588)4240945-7 gnd Kinetische Gleichung (DE-588)4030667-7 gnd Meinungsbildung (DE-588)4038461-5 gnd Mehragentensystem (DE-588)4389058-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Komplexes System (DE-588)4114261-5 gnd Schwarmverhalten (DE-588)4180330-9 gnd Mathematische Modellierung (DE-588)7651795-0 gnd Kollektives Verhalten (DE-588)4130047-6 gnd Vermögensverteilung (DE-588)4063086-9 gnd |
| topic_facet | Monte-Carlo-Simulation Kinetische Gleichung Meinungsbildung Mehragentensystem Mathematisches Modell Komplexes System Schwarmverhalten Mathematische Modellierung Kollektives Verhalten Vermögensverteilung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027002439&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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