财富分布演化的非麦克斯韦动力学方程
Non-Maxwellian kinetic equations modeling the evolution of wealth distribution
摘要：
我们引入了一类新的一维线性Fokker-Planck型方程，描述了多智能体社会中财富随时间的演化。通过标准的限制程序，通过对Cordier，Pareschi和Toscani根据Bouchaud和Mézard先前的研究于2005年引入的动力学模型引入经济相关的变体来获得方程。由这些新的福克-普朗克方程预测的财富稳定状态相对于原始福克-普朗克方程的稳定状态保持不变。然而，与原方程不同，它被证明是一个新的对数Sobolev不等式的重量和经典的熵方法，该解决方案指数快速收敛到平衡。
英文摘要：
We introduce a class of new one-dimensional linear Fokker--Planck type equations describing the evolution in time of the 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.
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