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Asymptotic Behavior of First Passage Probabilities in the Perturbed Non-homogeneous Semi-Markov Systems

Abstract In the present we study the asymptotic behavior of the sequence of the first passage probability matrices in a Perturbed Non-Homogeneous Semi-Markov System (P-NHSMS). We study initially triple sequences of matrices and we establish a basic result which provides the conditions under which the triple limit of a sequence coinsides. Then we provide some theorems which establish the asymptotic behavior of the sequence of matrices of the expected probabilities of first visit in a state in a given interval with a specified number of transitions.