Abstract
In this article, we show that the well-known Helmert matrix has strong relationship with stochastic matrices in modern probability theory. In fact, we show that we can construct some stochastic matrices by the Helmert matrix. Hence, we introduce a new class of regular and doubly stochastic matrices by use of the Helmert matrix and a special diagonal matrix that is defined in this article. Afterwards, we obtain the stationary distribution for this new class of stochastic matrices.
Highlights
In modern probability theory and dynamical systems, stochastic processes and Markov chains are applied contexts that are used in advanced sciences
We can working on many topics of probability theory, but working on stochastic processes and offering new Markov chains are less than other subjects
In this article we presented a new class of stochastic matrices
Summary
In modern probability theory and dynamical systems, stochastic processes and Markov chains are applied contexts that are used in advanced sciences. Two basic topics in stochastic process are prediction and filtering. This work is done by a matrix which is called the stochastic or probability or transition or Markov matrix. In stochastic processes or Markov chains, stochastic matrices are used for showing the transition probabilities [9, 11]. A Helmert matrix of order is a square matrix that was introduced by H. We will show that the Helmert matrix can be used in stochastic processes. (a) denotes an identity matrix of order. (b) denotes an × matrix whose elements are all 1. (c) denotes the inverse of a matrix. (d) denotes the transpose of a matrix.
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