Two-Point Probability Functions and Correlation Properties of the Generalized Additive High-Order Markov Chains

The aim of this work is to study statistical properties of the finite state Markov chains of the Nth order which have a vast area of applications as modeling and algorithmic tools in computer science, communication and network system analysis and development, risk management and decision making problems, etc. The transition probability matrix of the chain is assumed to be homogeneous and additive, with arbitrary form of memory functions. We obtain analytical solutions for the stationary probability distribution vector and for the correlation matrix and, thus, for the two-point probability distribution functions of the chain.