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趋势跟随与反对行为下的随机观点扩散

文章 arXiv papers · 作者: Manuel González-Navarrete
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总结

本文提出一个随机模型，描述趋势跟随者、反对者和无倾向者组成的人群中观点如何传播。强化机制影响智能体的选择，未观测到的趋势过程则塑造这些决策。该框架表示了观点形成中的放大、抵制和随机性。

分析推导了各类智能体数量的有限时间矩，并确立了渐近结果，包括大数定律、中心极限定理行为、重对数结果和经验比例的收敛。推导采用鞅方法，作者报告了重要量的闭式表达式。本文强调，初始随机差异可能持续存在，也可能消退，具体取决于强化和反对的相对强度。本文提供的数学工具或可用于社会、营销或信息扩散过程的模拟，但没有提供实证市场证据或直接交易策略。

核心观点

  • 观点扩散模型涵盖趋势跟随者、反对者和无倾向者。
  • 强化机制和潜在趋势共同塑造智能体的决策。
  • 分析给出了有限时间矩和多项大样本收敛结果。
  • 早期随机波动是否持续，取决于强化与反对之间的平衡。
  • 这些结果属于理论研究，不能确立金融市场策略。

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统计学
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# A stochastic model for the diffusion of competing opinions with trend-following, opposition, and indifference


# A stochastic model for the diffusion of competing opinions with trend-following, opposition, and indifference









We study a stochastic model for the diffusion of competing opinions in a population composed of three types of agents: trend-followers, opposers, and indifferent individuals. The decision dynamics are driven by reinforcement mechanisms, modulated by a latent trend process, allowing us to capture realistic features such as amplification, resistance, and randomness in opinion formation. We derive explicit formulas for the finite-time moments of the opinion count vector and establish a set of strong asymptotic results, including laws of large numbers, central limit theorems, laws of the iterated logarithm, and almost sure convergence of empirical distributions. In particular, we show how early fluctuations can persist or vanish depending on the balance between reinforcement and opposition. Our analysis relies on martingale techniques and offers closed-form expressions for key quantities, providing both theoretical insights and tools for simulations or applications in social dynamics, marketing, or information diffusion.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。