On a Fokker-Planck equation for wealth distribution

Marco Torregrossa; Giuseppe Toscani

doi:10.3934/krm.2018016

Article Contents

2018, Volume 11, Issue 2: 337-355. Doi: 10.3934/krm.2018016

This issue Previous Article A Vlasov-Poisson plasma of infinite mass with a point charge Next Article Invariant measures for a stochastic Fokker-Planck equation

On a Fokker-Planck equation for wealth distribution

Marco Torregrossa^1, , and
Giuseppe Toscani^2,

1.
Department of Mathematics, University of Pavia, Pavia, Italy
2.
Department of Mathematics, University of Pavia, and IMATI-CNR, Pavia, Italy

* Corresponding authorr: Marco Torregrossa
* Corresponding authorr: Marco Torregrossa

Received: December 31, 2016

Revised: April 30, 2017

Published: March 2018

This work has been written within the activities of the National Group of Mathematical Physics (GNFM) of INdAM (National Institute of High Mathematics), and partially supported by the MIUR-PRIN Grant 2015PA5MP7 "Calculus of Variations"

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Abstract

We study here a Fokker-Planck equation with variable coefficient of diffusion and boundary conditions which appears in the study of the wealth distribution in a multi-agent society [2, 10, 22]. In particular, we analyze the large-time behavior of the solution, by showing that convergence to the steady state can be obtained in various norms at different rates.

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Mathematics Subject Classification: Primary: 91D10; Secondary: 35Q84, 82B21, 94A17.

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