The representation of high order Markov process through equivalent first order process

Abstract

The expanded transition probability matrix with size of S Sn  S is used to represent n-order Markov process, which consists of S components, through first order process. With growth of process order the matrix size increases rapidly and a lot of resources are needed to store it, although many of its elements are zero. In this paper we propose to split states of Markov processes to "fictitious" depending on the model order, which can significantly reduce the size of the transition probability matrix.