We present and discuss various one-dimensional linear Fokker-Planck-Type equations that have been recently considered in connection with the study of interacting multi-Agent systems. In general, these Fokker-Planck equations describe the evolution in time of some probability density of the population of agents, typically the distribution of the personal wealth or of the personal opinion, and are mostly obtained by linear or bilinear kinetic models of Boltzmann type via some limit procedure. The main feature of these equations is the presence of variable diffusion, drift coefficients and boundaries, which introduce new challenging mathematical problems in the study of their long-Time behavior.

Fokker-Planck equations in the modeling of socio-economic phenomena / G. Furioli, A. Pulvirenti, E. Terraneo, G. Toscani. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 27:1(2017), pp. 115-158. [10.1142/S0218202517400048]

Fokker-Planck equations in the modeling of socio-economic phenomena

E. Terraneo
Penultimo
;
2017

Abstract

We present and discuss various one-dimensional linear Fokker-Planck-Type equations that have been recently considered in connection with the study of interacting multi-Agent systems. In general, these Fokker-Planck equations describe the evolution in time of some probability density of the population of agents, typically the distribution of the personal wealth or of the personal opinion, and are mostly obtained by linear or bilinear kinetic models of Boltzmann type via some limit procedure. The main feature of these equations is the presence of variable diffusion, drift coefficients and boundaries, which introduce new challenging mathematical problems in the study of their long-Time behavior.
Kinetic models; Fokker-Planck equations; relative entropies; large-time behavior
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/512154
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