Memory Function versus Binary Correlator in Additive Markov Chains

TL;DR

This paper explores the relationship between the memory function and pair correlator in additive binary Markov chains, providing a new method to analyze their global statistical properties and long-range correlations.

Contribution

It introduces a novel approach linking the memory function with the pair correlator through an integral equation, enhancing understanding of binary chain correlations.

Findings

Derived integral equation connecting memory function and pair correlator

Analyzed specific cases with potential applications in various fields

Provided detailed analysis of short and long-range correlations

Abstract

We study properties of the additive binary Markov chain with short and long-range correlations. A new approach is suggested that allows one to express global statistical properties of a binary chain in terms of the so-called memory function. The latter is directly connected with the pair correlator of a chain via the integral equation that is analyzed in great detail. To elucidate the relation between the memory function and pair correlator, some specific cases were considered that may have important applications in different fields.