论文标题
一美元交换生态植物物理学模型的混乱统一繁殖
Uniform propagation of chaos for a dollar exchange econophysics model
论文作者
论文摘要
我们研究了[2]中引入的货币兑换的偏差模型：代理人以与当前财富成正比的速度随机挑选，然后选定的代理商向另一个代理商提供了一美元，以随机统一选择。在[2,16]中对有限的许多代理以及严格分析的随机系统进行的模拟表明，当代理和时间的数量变得足够大时，代理之间的货币分布会收敛到泊松分布。在本手稿中，我们建立了混乱的统一传播，因为代理的数量进入无穷大，这证明了普通微分方程的平均场确定性无限系统的有效性是基于基于随机剂的基于基于随机剂的近似值。
We study the poor-biased model for money exchange introduced in [2]: agents are being randomly picked at a rate proportional to their current wealth, and then the selected agent gives a dollar to another agent picked uniformly at random. Simulations of a stochastic system of finitely many agents as well as a rigorous analysis carried out in [2,16] suggest that, when both the number of agents and time become large enough, the distribution of money among the agents converges to a Poisson distribution. In this manuscript, we establish a uniform-in-time propagation of chaos result as the number of agents goes to infinity, which justifies the validity of the mean-field deterministic infinite system of ordinary differential equations as an approximation of the underlying stochastic agent-based dynamics.
