Feller扩散中的统计混合和聚集
Statistical mixing and aggregation in Feller diffusion
摘要：
我们考虑Feller均值回复平方根扩散，它已被应用于模拟各种各样的过程与线性状态相关的扩散，如随机波动率和利率在金融，神经元和种群动力学在自然科学。我们专注于统计混合（或超统计）的过程中，与平均值相关的参数可以波动-出现重尾分布的一个合理的机制。我们得到相关的概率密度函数（固定和时间依赖），其相关结构和聚集特性的分析结果。我们的结果被应用于解释不同聚集尺度下股票交易量的统计。
英文摘要：
We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and populations dynamics in natural sciences. We focus on the statistical mixing (or superstatistical) process in which the parameter related to the mean value can fluctuate - a plausible mechanism for the emergence of heavy-tailed distributions. We obtain analytical results for the associated probability density function (both stationary and time dependent), its correlation structure and aggregation properties. Our results are applied to explain the statistics of stock traded volume at different aggregation scales.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
