We introduce a class of new one-dimensional linear Fokker-Planck-type equations describing the dynamics of the distribution of wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an economically relevant variant to the kinetic model introduced in 2005 by Cordier, Pareschi and Toscani according to previous studies by Bouchaud and Mézard. The steady state of wealth predicted by these new Fokker-Planck equations remains unchanged with respect to the steady state of the original Fokker-Planck equation. However, unlike the original equation, it is proven by a new logarithmic Sobolev inequality with weight and classical entropy methods that the solution converges exponentially fast to equilibrium.

(2020). Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution [journal article - articolo]. In MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. Retrieved from http://hdl.handle.net/10446/158623

Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

Furioli, G.;
2020-01-01

Abstract

We introduce a class of new one-dimensional linear Fokker-Planck-type equations describing the dynamics of the distribution of wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an economically relevant variant to the kinetic model introduced in 2005 by Cordier, Pareschi and Toscani according to previous studies by Bouchaud and Mézard. The steady state of wealth predicted by these new Fokker-Planck equations remains unchanged with respect to the steady state of the original Fokker-Planck equation. However, unlike the original equation, it is proven by a new logarithmic Sobolev inequality with weight and classical entropy methods that the solution converges exponentially fast to equilibrium.
articolo
2020
Furioli, Giulia Maria Dalia; Pulvirenti, A.; Terraneo, E.; Toscani, G.
(2020). Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution [journal article - articolo]. In MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. Retrieved from http://hdl.handle.net/10446/158623
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/158623
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