On steady distributions of kinetic models of conservative economies

Journal of Statistical Physics

Volumn 130, Issue 6, 2008, Pages 1087-1117

  Matthes, Daniel ^a   Toscani, Giuseppe ^b  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

^b UNIVERSITY OF PAVIA   (Italy)

Author keywords

Boltzmann equation; Econophysics; Pareto distribution; Wealth and income distributions

Indexed keywords

EID: 39149109342     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-007-9462-2     Document Type: Article

References (42)

1. Bisi, M., Carrillo, J.A., Toscani, G.: Contractive Metrics for a Boltzmann equation for granular gases: Diffusive equilibria. J. Stat. Phys. 118(1-2), 301-331 (2005)
2. Bisi, M., Carrillo, J.A., Toscani, G.: Decay rates in probability metrics towards homogeneous cooling states for the inelastic Maxwell model. J. Stat. Phys. 124(2-4), 625-653 (2006)
3. Bobylev, A.V.: The theory of the spatially Uniform Boltzmann equation for Maxwell molecules. Sov. Sci. Rev. C 7, 112-229 (1988)
4. Bobylev, A.V., Carrillo, J.A., Gamba, I.: On some properties of kinetic and hydrodynamics equations for inelastic interactions. J. Stat. Phys. 98, 743-773 (2000)
5. Bobylev, A.V., Cercignani, C.: Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions. J. Stat. Phys. 110, 333-375 (2003)
6. Bouchaud, J.P., Mézard, M.: Wealth condensation in a simple model of economy. Physica A 282, 536-545 (2000)
7. Carrillo, J.A., Toscani, G.: Contractive probability metrics and asymptotic behavior of dissipative kinetic equations. Riv. Mat. Univ. Parma 6, 75-198 (2007)
8. Cercignani, C., Illner, R., Pulvirenti, M.: The Mathematical Theory of Dilute Gases. Applied Mathematical Sciences, vol. 106. Springer, New York (1994)
9. Chakraborti, A.: Distributions of money in models of market economy. Int. J. Mod. Phys. C 13, 1315-1321 (2002)
10. Chakraborti, A., Chakrabarti, B.K.: Statistical mechanics of money: how saving propensity affects its distributions. Eur. Phys. J. B 17, 167-170 (2000)
11. Chatterjee, A., Chakrabarti, B.K., Manna, S.S.: Pareto law in a kinetic model of market with random saving propensity. Physica A 335, 155-163 (2004)
12. Chakraborti, A., Germano, G., Heinsalu, E., Patriarca, M.: Relaxation in statistical many-agent economy models. Eur. Phys. J. B 57, 219-224 (2007)
13. Cordier, S., Pareschi, L., Toscani, G.: On a kinetic model for a simple market economy. J. Stat. Phys. 120, 253-277 (2005)
14. Das, A., Yarlagadda, S.: Analytic treatment of a trading market model. Phys. Scr. T 106, 39-40 (2003)
15. Desvillettes, L., Furioli, G., Terraneo, E.: Propagation of Gevrey regularity for solutions of Boltzmann equation for Maxwellian molecules. Trans. Am. Math. Soc. (in press)
16. Di Matteo, T., Aste, T., Hyde, S.T.: In: Mallamace, F., Stanley, H.E. (eds.) The Physics of Complex Systems (New Advances and Perspectives). IOS Press, Amsterdam (2004)
17. Drgulescu, A., Yakovenko, V.M.: Statistical mechanics of money. Eur. Phys. J. B 17, 723-729 (2000)
18. Drgulescu, A., Yakovenko, V.M.: Exponential and power law probability distribution of wealth and income in the United Kingdom and the United States. Physica A 299, 213-221 (2001)
19. Düring, B., Toscani, G.: Hydrodynamics from kinetic models of conservative economies. Physica A 384, 493-506 (2007)
20. Ernst, M.H., Brito, R.: High energy tails for inelastic Maxwell models. Europhys. Lett. 43, 497-502 (2002)
21. Ernst, M.H., Brito, R.: Scaling solutions of inelastic Boltzmann equation with over-populated high energy tails. J. Stat. Phys. 109, 407-432 (2002)
22. Gabetta, E., Toscani, G., Wennberg, B.: Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation. J. Stat. Phys. 81, 901-934 (1995)
23. Gamba, I.M., Rjasanow, S., Wagner, W.: Direct simulation of the uniformly heated granular Boltzmann equation. Math. Comput. Model. 42, 683-700 (2005)
24. Gosse, L., Toscani, G.: Identification of asymptotic decay to self-similarity for one-dimensional filtration equations. SIAM J. Numer. Anal. 43(6), 2590-2606 (2006)
25. Hayes, B.: Follow the money. Am. Sci. 90(5), 400-405 (2002)
26. Ispolatov, S., Krapivsky, P.L., Redner, S.: Wealth distributions in asset exchange models. Eur. Phys. J. B 2, 267-276 (1998)
27. Kac, M.: Probability and Related Topics in the Physical Sciences. Interscience Publishers, New York (1959)
28. Levy, M., Solomon, S.: New evidence for the power-law distribution of wealth. Physica A 242, 90-94 (1997)
29. Levy, H., Levy, M., Solomon, S.: Microscopic Simulations of Financial Markets. Academic Press, New York (2000)
30. Malcai, O., Biham, O., Solomon, S., Richmond, P.: Theoretical analysis and simulations of the generalized Lotka-Volterra model. Phys. Rev. E 66, 031102 (2002)
31. Mandelbrot, B.: The Pareto-Lévy law and the distribution of income. Int. Econ. Rev. 1, 79-106 (1960)
32. Matthes, D., Toscani, G.: Analysis of a model for wealth redistribution. Preprint (2007)
33. Mohanty, P.K.: Generic features of the wealth distribution in an ideal-gas-like market. Phys. Rev. E 74(1), 011117 (2006)
34. Pareschi, L., Toscani, G.: Self-similarity and power-like tails in nonconservative kinetic models. J. Stat. Phys. 124(2-4), 747-779 (2006)
35. Pareto, V.: Cours d'Economie Politique. Lausanne and Paris (1897)
36. Patriarca, M., Chakraborti, A., Kaski, K.: Statistical model with a standard Γ distribution. Phys. Rev. E 70, 016104 (2004)
37. Pulvirenti, A., Toscani, G.: Asymptotic properties of the inelastic Kac model. J. Stat. Phys. 114, 1453-1480 (2004)
38. Repetowicz, P., Hutzler, S., Richmond, P.: Dynamics of money and income distributions. Physica A 356(2-4), 641-654 (2005)
39. Rjasanow, S.: Monte-Carlo methods for the Boltzmann equation. In: Degond, P., Pareschi, L., Russo, G. (eds.) Modeling and Computational Methods for Kinetic Equations, pp. 81-115. Birkhäuser Boston, Cambridge (2004)
40. Sinha, S.: The Rich Are Different!: Pareto Law from asymmetric interactions in asset exchange models. In: Chatterjee, A., Chakrabarti, B.K., Yarlagadda, S. (eds.) Econophysics of Wealth Distributions, pp. 177-184. Springer, New York (2005)
41. Slanina, F.: Inelastically scattering particles and wealth distribution in an open economy. Phys. Rev. E 69, 046102 (2004)
42. Solomon, S.: Stochastic Lotka-Volterra systems of competing auto-catalytic agents lead generically to truncated Pareto power wealth distribution, truncated Levy distribution of market returns, clustered volatility, booms and crashes. In: Refenes, A.P.N., Burgess, A.N., Moody, J.E. (eds.) Computational Finance 97. Kluwer Academic, Dordrecht (1998)