Fractional Langevin model of memory in financial time series.

Financial time series are random with the absolute value of the price index fluctuations having an inverse power-law correlation. A dynamical model of this behavior is proposed using a fractional Langevin equation. The physical basis for this model is the divergence of the microscopic time scale to overlap with the macroscopic time scale: a condition that is not observed in classical statistical mechanics. This time-scale separation provides a mechanism for the market to adjust the volitility of the price index fluctuations.