The Rotational Theory of Markov Processes
Up to this point of our exposition, it has been seen that the main geometric characteristics of either theoretical or practical importance for the definition of finite recurrent Markov processes are the edges and circuits. The cycle representation theory presented in Part I gives us the liberty to interchange the weighted edges (of the stochastic matrices) with the weighted cycles or circuits (of the circuit representations), and the resulting equations and new revelations in the interaction between the stochastic processes theory and algebraic topology are so useful that there is an unavoidable methodological horizon leading to edge-problems and cycle-problems.
KeywordsMarkov Process Betti Number Stochastic Matrix Stochastic Matrice Connectivity Relation
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