Full Randomness in the Higher Difference Structure of Two-state Markov Chains

2017/06/23 by Shahverdian, A. Yu.
#60J10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1706.07865

Abstract

The paper studies the higher-order absolute differences taken from progressive terms of time-homogenous binary Markov chains. Two theorems presented are the limiting theorems for these differences, when their order k converges to infinity. Theorems 1 and 2 assert that there exist some infinite subsets E of natural series such that kth order differences of every such chain converge to the equi-distributed random binary process as k growth to infinity remaining on E. The chains are classified into two types and E depend only on the type of a given chain. Two kinds of discrete capacities for subsets of natural series are defined, and in their terms such sets E are described.

Related

• Discrete Capacity and Higher-order Differences of Two-state Markov Chains
• On limiting probability distributions of higher order Markov chains
• Quantitative Convergence Rates for Stochastically Monotone Markov Chains
• Can a higher-order Markov chain be treated as a first-order Markov chain?
• Information divergences of Markov chains and their applications