Discrete Capacity and Higher-order Differences of Two-state Markov Chains

TL;DR

This paper investigates the properties of higher-order differences in two-state Markov chains, introducing a discrete capacity concept and establishing a limiting theorem akin to Wiener criteria.

Contribution

It introduces a novel discrete capacity framework and a limiting theorem for higher-order differences in two-state Markov chains, expanding theoretical understanding.

Findings

Defined a discrete capacity for subsets of natural numbers

Established a Wiener criterion type limiting theorem

Analyzed the behavior of higher-order differences in Markov chains

Abstract

The paper studies the time-homogeneous two-state Markov chains; the states are assumed to be binary symbols 0 and 1. The higher-order absolute differences taken from progressive states of a given chain are considered. A discrete capacity of subsets of natural series is defined and a limiting theorem for these differences, formulated in terms of Wiener criterion type relation, is presented.