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

TL;DR

This paper introduces nonlinear stochastic differential equations that produce q-exponential and q-Gaussian distributions along with 1/f^beta noise, linking nonextensive statistical mechanics to long-range correlated signals.

Contribution

It unifies modeling of nonextensive distributions with 1/f noise through a new class of nonlinear stochastic differential equations and superstatistical framework.

Findings

Derives stochastic equations yielding q-Gaussian distributions.

Reveals long-range correlations and 1/f^beta spectral behavior.

Connects nonextensive statistics with 1/f noise phenomena.

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.