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Matematicheskie Zametki, 1975, Volume 17, Issue 2, Pages 329–339 (Mi mzm7549)  
Additive functionals of semi-Markov processes with absorption

A. P. Cherenkov
Full-text PDF (684 kB)
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.
Received: 18.12.1973
English version:
Mathematical Notes, 1975, Volume 17, Issue 2, Pages 189–194
DOI: https://doi.org/10.1007/BF01161879
Bibliographic databases:
UDC: 519.2
Language: Russian
Citation: A. P. Cherenkov, “Additive functionals of semi-Markov processes with absorption”, Mat. Zametki, 17:2 (1975), 329–339; Math. Notes, 17:2 (1975), 189–194
Citation in format AMSBIB
\Bibitem{Che75}
\by A.~P.~Cherenkov
\paper Additive functionals of semi-Markov processes with absorption
\jour Mat. Zametki
\yr 1975
\vol 17
\issue 2
\pages 329--339
\mathnet{http://mi.mathnet.ru/mzm7549}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=423568}
\zmath{https://zbmath.org/?q=an:0361.60078}
\transl
\jour Math. Notes
\yr 1975
\vol 17
\issue 2
\pages 189--194
\crossref{https://doi.org/10.1007/BF01161879}
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