标题： 广义货币交换模型的极限分布 显示英文标题

标题： Limiting distributions of generalized money exchange models

摘要： “货币交换模型”是一种基于代理的模拟模型，用于研究个体之间的货币交换如何导致财富分配和不平等的演变。 该模型的主要重点是在给定代理之间交换的微观规则下，确定在宏观层面上出现的极限财富分布。 在本文中，我们将即时交换模型和均匀储蓄模型这两种货币交换模型的广义版本都表述为离散时间相互作用粒子系统，并描述它们的平稳分布。 此外，我们证明了在适当的缩放下，两种模型的渐近财富分布都收敛到伽马分布或指数分布。 极限分布取决于影响每个代理交换硬币数量的概率分布的权重函数。 特别是，我们的结果提供了之前基于数值模拟和启发式论证的研究中所预测的断言的数学严格表述和推广。 显示英文摘要

摘要： The "Money Exchange Model" is a type of agent-based simulation model used to study how wealth distribution and inequality evolve through monetary exchanges between individuals. The primary focus of this model is to identify the limiting wealth distributions that emerge at the macroscopic level, given the microscopic rules governing the exchanges among agents. In this paper, we formulate generalized versions of the immediate exchange model and the uniform saving model both of which are types of money exchange models, as discrete-time interacting particle systems and characterize their stationary distributions. Furthermore, we prove that under appropriate scaling, the asymptotic wealth distribution converges to a Gamma distribution or an exponential distribution for both models. The limiting distribution depends on the weight function that affects the probability distribution of the number of coins exchanged by each agent. In particular, our results provide a mathematically rigorous formulation and generalization of the assertions previously predicted in studies based on numerical simulations and heuristic arguments.