Statistical mixing and aggregation in Feller diffusion
arXiv:0910.1394 · doi:10.1088/1742-5468/2009/10/P10023
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.
16 pages, 3 figures. To be published in Journal of Statistical Mechanics: Theory and Experiment
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Cited by in corpus (6)
- Generalized statistical mechanics for superstatistical systems
- Superstatistical analysis of sealevel fluctuations
- Generalization of the Beck-Cohen superstatistics
- Intraday Seasonalities and Nonstationarity of Trading Volume in Financial Markets: Individual and Cross-Sectional Features
- Extreme Value Laws for Superstatistics
- Random diffusivity scenarios behind anomalous non-Gaussian diffusion