The size order of the state vector of discrete-time homogeneous Markov systems

Abstract

The size order problem of the probability state vector elements of a homogeneous Markov system is examined. The time t₀ is evaluated, after which the order of the state vector probabilities remains unchanged, and a formula to quickly find a lower bound for t₀ is given. A formula for approximating the mode of the state sizes n_i(t) as a function of the means En_i(t), and a relation to evaluate P(n_i(t) = x+1) by means of certain terms which constitute P(n_i(t) = x) are derived.