Long-range correlated stationary Markovian processes

Fabrizio Lillo; Salvatore Micciche'; Rosario N. Mantegna

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Long-range correlated stationary Markovian processes

Fabrizio Lillo·Salvatore Micciche'·Rosario N. Mantegna

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Abstract

We introduce a new class of stochastic processes which are stationary, Markovian and characterized by an infinite range of time-scales. By transforming the Fokker-Planck equation of the process into a Schrodinger equation with an appropriate quantum potential we determine the asymptotic behavior of the autocorrelation function of the process in an analytical way. We find the conditions needed to observe a stationary long-range correlated Markovian process. In the presence of long-range correlation, for selected values of the control parameters, the process has a 1/f-like spectral density for low frequency values.

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Fabrizio Lillo, Salvatore Micciche', Rosario N. Mantegna. 2002-03-21. Long-range correlated stationary Markovian processes. https://arxiv.org/abs/cond-mat/0203442

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