Abstract
Given a semi-Markov process with an arbitrary set of states, a criterion is obtained for the attainability of a certain isolated subset of states and for finiteness of the average attainment time. An equation is given for the average of an additive functional of a process with absorption, existence and uniqueness conditions are deduced for the solution of that equation in a given class of functions, and an integral representation is obtained for the solution.
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Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 329–339, February, 1975.
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Cherenkov, A.P. Additive functionals of semi-Markov processes with absorption. Mathematical Notes of the Academy of Sciences of the USSR 17, 189–194 (1975). https://doi.org/10.1007/BF01161879
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DOI: https://doi.org/10.1007/BF01161879