The entropy corrected geometric Brownian motion

Rishabh Gupta, Ewa Drzazga-Szczȩśniak, Sabre Kais, Dominik Szczȩśniak
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Abstract

The geometric Brownian motion (GBM) is widely employed for modeling stochastic processes, yet its solutions are characterized by the log-normal distribution. This comprises predictive capabilities of GBM mainly in terms of forecasting applications. Here, entropy corrections to GBM are proposed to go beyond log-normality restrictions and better account for intricacies of real systems. It is shown that GBM solutions can be effectively refined by arguing that entropy is reduced when deterministic content of considered data increases. Notable improvements over conventional GBM are observed for several cases of non-log-normal distributions, ranging from a dice roll experiment to real world data.
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熵校正几何布朗运动
几何布朗运动(GBM)被广泛用于模拟随机过程,但其解的特征是对数正态分布。这使得 GBM 的预测能力主要局限于预测应用。本文提出了对 GBM 的熵修正,以超越对数正态性限制,更好地解释错综复杂的真实系统。研究表明,当考虑数据的确定性内容增加时,熵会减少,因此可以有效地完善 GBM 解决方案。从掷骰子实验到真实世界的数据,在非对数正态分布的几种情况下,与传统的 GBM 相比都有显著的改进。
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