We consider a singularly perturbed (finite state) Markov chain and provide a complete characterization of the fundamental matrix. In particular, we obtain a formula for the regular part simpler than a ...

High-order Markov chain models extend the conventional framework by incorporating dependencies that span several previous states rather than solely the immediate past. This extension allows for a ...

Abstract Let 𝜉 = {𝜉𝑛}𝑛≥₀ be a Markov chain defined on a probability space (Ω, ℱ, ℙ) valued in a discrete topological space 𝑆 that consists of a finite number of real 𝑑 × 𝑑 matrices. As usual, ...

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