Inequality of Realization of a Stochastic Dynamics Based on the Erdös Discrepancy Problem

• 作者: Hiroyuki Kato
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Erd?s DISCREPANCY PROBLEM ARITHMETIC PROGRESSION INEQUALITY Economic Dynamics
• 年，卷（期）: 2019,（10）
• 页码范围: 836-847
• 页数: 12页
• 分类号: O17

摘要

This paper proposes a stochastic dynamics model in which people who are endowed with different discount factors chose to buy the capital stock periodically with different periodicities and are exposed to randomness at arithmetic progression times. We prove that the realization of a stochastic equilibrium may render to the people quite unequal benefits. Its proof is based on Erdös Discrepancy Problem that an arithmetic progression sum of any sign sequence goes to infinity, which is recently solved by Terence Tao [1]. The result in this paper implies that in some cases, the sources of inequality come from pure luck.