Helmert Matrix and its Consequences in Stochastic Processes

In this article, we want to show that the Helmert matrix has strong relationship with stochastic matrixes in modern probability theory. In fact, we want to show that we can build a stochastic matrix by Helmert matrix. Initial, we want to prove that if be the Helmert matrix of order n, then is a stochastic matrix and afterward we prove that the Markov chain by this stochastic matrix is regular and ergodic

Keywords:

Helmert matrix , stochastic matrix , Markov chain , transition probability