Full randomness in the higher difference structure of two-state Markov chains

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.

State space classification of Markov password – an alphanumeric password authentication scheme for secure communication in cloud computing

“…They addressed this dynamical diesel engine mechanism problem with Markov chain evaluation and obtained optimized solution compared with other methods such as neural network assessment, analytical regression and grey forecast method (Yong et al, 2011). Shahverdian (2017) studied the ergodicity property of Markov chain and came up with classification of time homogeneous Markov chain in to type I and II. The necessary and convergence criteria of those were derived with illustrations (Shahverdian, 2017).…”

“…Shahverdian (2017) studied the ergodicity property of Markov chain and came up with classification of time homogeneous Markov chain in to type I and II. The necessary and convergence criteria of those were derived with illustrations (Shahverdian, 2017). Barbu (2013) studied the application of Markov chain in endurance analysis and problems in reliability.…”