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arXiv · 1706.07865

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

A. Yu. Shahverdian
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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 $k$th 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.

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A. Yu. Shahverdian. 2017-06-23. Full Randomness in the Higher Difference Structure of Two-state Markov Chains. https://arxiv.org/abs/1706.07865

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