A random telegraph signal of Mittag-Leffler type

TL;DR

This paper introduces a method to compute autocovariance functions for non-Poisson dichotomous noise, specifically applied to Mittag-Leffler type signals, highlighting the limitations of standard spectral methods for non-stationary noise.

Contribution

It presents a novel explicit computation method for autocovariance functions of non-Poisson dichotomous noise, with a focus on Mittag-Leffler type signals, and compares analytical results with simulations.

Findings

Analytical autocovariance functions match Monte Carlo simulations.

Standard spectral methods are inadequate for non-stationary non-Poisson noise.

The method provides insights into non-stationary dichotomous noise behavior.

Abstract

A general method is presented to explicitly compute autocovariance functions for non-Poisson dichotomous noise based on renewal theory. The method is specialized to a random telegraph signal of Mittag-Leffler type. Analytical predictions are compared to Monte Carlo simulations. Non-Poisson dichotomous noise is non-stationary and standard spectral methods fail to describe it properly as they assume stationarity.