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.File | Dimensione del file | Formato | |
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2020-FPTT-nonmaxwellian-M3AS.pdf
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Fokker-New.pdf
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Descrizione: “Electronic version of an article published as [Mathematical Models and Methods in Applied Sciences 2020 30:04, 685-725] [DOI 10.1142/S0218202520400023] © [copyright World Scientific Publishing Company] [https://www.worldscientific.com/worldscinet/m3as] The Digital Object Identifier (DOI) of your article can be found on the relevant webpage of WorldSciNet where your article is posted.”
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