Geodesic
Additive functionals of regular semi-Markov processes
Matematičeskie zametki, Tome 18 (1975) no. 4, pp. 621-631

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The behavior of the mean values of additive functionals of regular semi-Markov processes with arbitrary (not necessarily finite or countable) sets of states is studied. An integral representation of the mean value of an additive functional is obtained. The behavior of certain operators connected with the process is investigated. As as illustration of the possible applications of the results obtained here we formulate and prove a limit theorem for a semi-Markov process. See [7]. 
@article{MZM_1975_18_4_a15,
     author = {A. P. Cherenkov},
     title = {Additive functionals of regular {semi-Markov} processes},
     journal = {Matemati\v{c}eskie zametki},
     pages = {621--631},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a15/}
}
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A. P. Cherenkov. Additive functionals of regular semi-Markov processes. Matematičeskie zametki, Tome 18 (1975) no. 4, pp. 621-631. http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a15/