Statistical mixing and aggregation in Feller diffusion

TL;DR

This paper analyzes the Feller diffusion process with fluctuating parameters, deriving analytical results for its probability density, correlation, and aggregation, and applies these findings to model stock traded volume statistics.

Contribution

It provides new analytical insights into the superstatistical Feller process, linking parameter fluctuations to heavy-tailed distributions and stock volume behavior.

Findings

Derived explicit forms of the probability density function.

Analyzed the correlation structure of the process.

Applied results to explain stock traded volume statistics.

Abstract

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.