2002/03/21 by Fabrizio Lillo, Salvatore Micciche', Lillo, Fabrizio +4 · 1 citation
Decision Sciences · Physics and Astronomy · #FOS: Physical sciences #Probabilistic and Robust Engineering Design #Scientific Research and Discoveries #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.cond-mat/0203442
4 pages
arxiv created 2002/03/21 · openalex publication_date 2002/03/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.