A Statistical Solution to Markov Matrix Chains


Authors : Dr. Ismail Abbas

Volume/Issue : Volume 6 - 2021, Issue 2 - February

Google Scholar : http://bitly.ws/9nMw

Scribd : https://bit.ly/3t5uJxo

Abstract : In part 1, we propose a statistical technique to the solution of stationary eigenvectors of Markov chains that is more efficient and more precise than the classical algebraic method. However, it only fails when the Markov matrix is not invertible, which is also the case for the classical solution. In part 2, we propose an important principle valid for B-Matrix chains: [For a positive symmetric physical matrix, the sum of their eigenvalues powers is equal to the eigenvalue of their sum of the series of powers of the matrix]. This principle is validated numerically by the derivation of an important equation for the sum of the series of algebraic powers, namely

In part 1, we propose a statistical technique to the solution of stationary eigenvectors of Markov chains that is more efficient and more precise than the classical algebraic method. However, it only fails when the Markov matrix is not invertible, which is also the case for the classical solution. In part 2, we propose an important principle valid for B-Matrix chains: [For a positive symmetric physical matrix, the sum of their eigenvalues powers is equal to the eigenvalue of their sum of the series of powers of the matrix]. This principle is validated numerically by the derivation of an important equation for the sum of the series of algebraic powers, namely

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