Tsallis distributions and 1/f noise from nonlinear stochastic differential equations

Abstract

Probability distributions which emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this paper we unite modeling of such distributions with the model of widespread 1/f noise. We propose a class of nonlinear stochastic differential equations giving both the q-exponential or q-Gaussian distributions of signal intensity, revealing long-range correlations and 1/f^beta behavior of the power spectral density. The superstatistical framework to get 1/f^beta noise with q-exponential and q-Gaussian distributions of the signal intensity in is proposed, as well.

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• Intermittency in relation with 1/f noise and stochastic differential equations
• The consentaneous model of the financial markets exhibiting spurious nature of long-range memory
• Interplay between endogenous and exogenous fluctuations in financial markets
• 1/f noise from point process and time-subordinated Langevin equations
• Understanding the nature of the long-range memory phenomenon in socioeconomic systems
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• Long-range memory test by the burst and inter-burst duration distribution
• Scaling theory for the $1/f$ noise