Interacting multiagent systems : kinetic equations and Monte Carlo methods / Lorenzo Pareschi, Giuseppe Toscani.

Format:

Book

Author/Creator:

Pareschi, Lorenzo.

Contributor:

Toscani, Giuseppe.

Language:

English

Subjects (All):

Monte Carlo method.

Equations of motion.

Multiagent systems--Mathematical models.

Multiagent systems.

Physical Description:

1 online resource (391 p.)

Edition:

First edition.

Place of Publication:

Oxford, [England] : Oxford University Press, 2014.

Language Note:

English

Summary:

The description of emerging collective phenomena and self-organization in systems composed of large numbers of individuals has gained increasing interest from various research communities in biology, ecology, robotics and control theory, as well as sociology and economics.Applied mathematics is concerned with the construction, analysis and interpretation of mathematical models that can shed light on significant problems of the natural sciences as well as our daily lives. To this set of problems belongs the description of the collective behaviours of complex systems composed by a large enough n

Contents:

Cover; Contents; Part I Kinetic modelling and simulation; 1 A short introduction to kinetic equations; 1.1 Boltzmann's legacy; 1.2 Notation; 1.3 Some linear kinetic models; 1.4 Binary interaction models on the real line; 1.5 Binary interaction models on the half-line; 1.6 Some classical results; 2 Mathematical tools; 2.1 How to be certain of the predictions of a model?; 2.2 Some mathematical tools; 2.3 The drift equation and Dirac delta functions; 2.4 Dissipative models and the drift equation; 2.5 Growth processes; 3 Monte Carlo strategies; 3.1 Why Monte Carlo methods?

3.2 Generating random variables3.3 Monte Carlo techniques; 3.4 Applications to evolutionary PDEs; 4 Monte Carlo methods for kinetic equations; 4.1 The general framework; 4.2 Relaxation problems; 4.3 Binary interaction models; 4.4 Asymptotic preserving Monte Carlo; 4.5 Kinetic approximation of diffusion equations; 4.6 Remarks on multi-dimensional problems; Part II Multiagent kinetic equations; 5 Models for wealth distribution; 5.1 Wealth, trades and kinetic equations; 5.2 Economic and kinetic dictionaries; 5.3 Kinetic market models for conservative economies

5.4 Non-conservative kinetic market models5.5 Exact solutions; 5.6 Modelling heterogeneous traders; 5.7 Individual preferences; 5.8 Taxation and wealth redistribution; 6 Opinion modelling and consensus formation; 6.1 Opinion formation; 6.2 Kinetic models of opinion formation; 6.3 Other Fokker-Planckmodels of opinion formation; 6.4 Choice formation and influence of external factors; 6.5 Opinion formation in the presence of leaders; 7 A further insight into economics and social sciences; 7.1 Towards more realistic models; 7.2 A kinetic model for trading goods

7.3 Modelling speculative nancial markets7.4 A model for different groups of traders; 7.5 Inhomogeneous models for the evolution of wealth; 8 Modelling in life sciences; 8.1 The Luria- Delbrück distribution; 8.2 The quasi-invariant limit of the growth of mutant cells; 8.3 Self-organized systems and swarming models; 8.4 Systems interacting with few individuals; 8.5 Final remarks; Appendix A Basic arguments on Fourier transforms; A.1 Definitions; A.2 Properties of the Fourier transform; Appendix B Important probability distributions; B.1 Uniform distribution; B.2 Beta distribution

B.3 Normal distributionB.4 Exponential distribution; B.5 Gamma distribution; B.6 Bernoulli distribution; B.7 Poisson distribution; List of figures; References; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

0-19-162887-5

0-19-162798-4

OCLC:

868597755