Description of all limit distributions of some Markov chains with memory 2

Abstract

There are situations where the data sequence does not depend on past values. As can be expected, the additional history of memory often has the advantage of offering a more precise predictive value. By bringing more memory into the random process, one can build a higher order Markov model. In this paper we consider 2-state Markov chain with memory 2 generated by Hamiltonian with competing interactions and describe its all limit distributions.