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Interacting Multiagent Systems Kinetic equations and Monte Carlo methods,9780199655465
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Interacting Multiagent Systems Kinetic equations and Monte Carlo methods

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Pub. Date:
Oxford University Press

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Author Biography

Lorenzo Pareschi, Full Professor of Numerical Analysis, Department of Mathematics and Computer Science, University of Ferrara, Italy,Giuseppe Toscani, Full Professor of Mathematical Physics, Department of Mathematics, University of Pavia, Italy

Lorenzo Pareschi is full professor of numerical analysis at the University of Ferrara. He holds a PhD in mathematics from Bologna University (1996). He is a leading expert in computational methods and modelling for nonlinear partial differential equations. His research interests include kinetic equations, hyperbolic conservation laws and relaxation systems, stiff systems and Monte Carlo methods. He has co-written three books and more than one hundred peer-reviewed articles. He serves as an associate editor for the SIAM Journal of Scientific Computing (SISC), Multiscale Modelling and Simulation (MMS), Kinetic and Related Models (KRM) and Communications in Mathematical Sciences (CMS). He held visiting professor positions at the University of Wisconsin, Madison (USA), the Georgia Institute of Technology, Atlanta, (USA), the University of Orleans (France) and the University of Toulouse (France). He is the chairman of the Department of Mathematics and Computer Science at the University of Ferrara.

Giuseppe Toscani is full professor of mathematical physics at the University of Pavia. His recent scientific interests are concerned with theoretical and numerical problems connected to the kinetic theory of rarefied gases, asymptotic behaviour of nonlinear diffusion equations by entropy methods, and kinetic modelling of socio-economic multi-agents systems. He has authored around 200 papers, written both individually or jointly with national and international experts, as well as two monographs on the mathematical aspects of Boltzmann equation and of Enskog equation in kinetic theory of rarefied gases. He held visiting professor positions at the Georgia Institute of Technology, Atlanta, (USA), and at the Universities of Paris VI, Paris Dauphine, Nice and Toulouse (France).

Table of Contents

1. A short introduction to kinetic equations
2. Mathematical tools
3. Monte Carlo strategies
4. Monte Carlo methods for kinetic equations
5. Models for wealth distribution
6. Opinion modelling and consensus formation
7. A further insight into economy and social sciences
8. Modelling in life sciences
Appendix A: Basic arguments on Fourier transforms
Appendix B: Important probability distributions

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