Interacting multiagent systems : kinetic equations and Monte Carlo methods /

Interacting multiagent systems : kinetic equations and Monte Carlo methods /

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 con...

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Bibliographic Details
Main Authors: Pareschi, Lorenzo (Author), Toscani, Giuseppe (Author)
Format: Electronic eBook
Language:English
Published: Oxford : Oxford University Press, 2014.
Edition:First edition.
Subjects:
Monte Carlo method.
Equations of motion.
Multiagent systems > Mathematical models.
Online Access:CONNECT
Table of Contents:
  • Machine generated contents note: 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 variables
  • 3.3. 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
  • 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 models
  • 5.5. 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-Planck models 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 financial markets
  • 7.4. 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
  • A.1. Definitions
  • A.2. Properties of the Fourier transform
  • B.1. Uniform distribution
  • B.2. Beta distribution
  • B.3. Normal distribution
  • B.4. Exponential distribution
  • B.5. Gamma distribution
  • B.6. Bernoulli distribution
  • B.7. Poisson distribution.

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