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Izv. Akad. Nauk SSSR Ser. Mat., 1969, Volume 33, Issue 4, Pages 861–900 (Mi izv2184)  

This article is cited in 15 scientific papers (total in 15 papers)

Factorization methods and boundary problems for sums of random variables given on Markov chains

E. L. Presman


Abstract: This work concerns asymptotic study of the joint distribution of the maximum of a sequence of sums and the sums themselves on finite regular Markov chains. To this end, a series of lemmas are demonstrated on factorization of elements of general algebraic rings, as well as factorization identities having interest in themselves which provide a connection between various distributions pertaining to the random processes in question.

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English version:
Mathematics of the USSR-Izvestiya, 1969, 3:4, 815–852

Bibliographic databases:

UDC: 519.2
MSC: 60G50, 60B15, 60J50, 60E05, 40A05
Received: 17.06.1968

Citation: E. L. Presman, “Factorization methods and boundary problems for sums of random variables given on Markov chains”, Izv. Akad. Nauk SSSR Ser. Mat., 33:4 (1969), 861–900; Math. USSR-Izv., 3:4 (1969), 815–852

Citation in format AMSBIB
\Bibitem{Pre69}
\by E.~L.~Presman
\paper Factorization methods and boundary problems for sums of random
variables given on Markov chains
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1969
\vol 33
\issue 4
\pages 861--900
\mathnet{http://mi.mathnet.ru/izv2184}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=256467}
\zmath{https://zbmath.org/?q=an:0192.55102|0208.43702}
\transl
\jour Math. USSR-Izv.
\yr 1969
\vol 3
\issue 4
\pages 815--852
\crossref{https://doi.org/10.1070/IM1969v003n04ABEH000802}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. H. Kaspi, “On the symmetric Wiener-Hopf factorization for Markov additive processes”, Z Wahrscheinlichkeitstheorie verw Gebiete, 59:2 (1982), 179  crossref  mathscinet  zmath
    2. J.H.A. de Smit, “The single server semi-Markov queue”, Stochastic Processes and their Applications, 22:1 (1986), 37  crossref
    3. Søren Asmussen, “Risk theory in a Markovian environment”, Scandinavian Actuarial Journal, 1989:2 (1989), 69  crossref
    4. V. S. Lugavov, “On factorization components of the sojourn times for semicontinuous random walks in a strip”, Siberian Math. J., 44:4 (2003), 629–637  mathnet  crossref  mathscinet  zmath  isi
    5. J. M. Reinhard, M. Snoussi, “A monotonically converging algorithm for the severity of ruin in a discrete semi-Markov risk model”, Scandinavian Actuarial Journal, 2004:5 (2004), 336  crossref
    6. V. I. Lotov, N. G. Orlova, “Factorization representations in the boundary crossing problems for random walks on a Markov chain”, Siberian Math. J., 46:4 (2005), 661–667  mathnet  crossref  mathscinet  zmath  isi
    7. V. I. Lotov, N. G. Orlova, “Asymptotic expansions for the distribution of the crossing number of a strip by a Markov-modulated random walk”, Siberian Math. J., 47:6 (2006), 1066–1083  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    8. M. S. Sgibnev, “The matrix analogue of the Blackwell renewal theorem on the real line”, Sb. Math., 197:3 (2006), 369–386  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. A. F. Voronin, “O korrektnosti integralnykh uravnenii v svertkakh na konechnom intervale i sistemy singulyarnykh integralnykh uravnenii s yadrom Koshi [Itogovyi nauchnyi otchet po mezhdistsiplinarnomu integratsionnomu proektu SO RAN: “Razrabotka teorii i vychislitelnoi tekhnologii resheniya obratnykh i ekstremalnykh zadach s prilozheniem v matematicheskoi fizike i gravimagnitorazvedke”]”, Sib. elektron. matem. izv., 5 (2008), 456–464  mathnet  mathscinet
    10. M. S. Sgibnev, “Semimultiplicative moments of factors in Wiener–Hopf matrix factorization”, Sb. Math., 199:2 (2008), 277–290  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. A. F. Voronin, A. E. Kovtanyuk, M. M. Lavrentev, “Kraevaya zadacha Rimana v issledovanii korrektnosti lineinykh i nelineinykh zadach matematicheskoi fiziki”, Sib. elektron. matem. izv., 7 (2010), 112–122  mathnet
    12. Emile Le Page, Yinna Ye, “The survival probability of a critical branching process in a Markovian random environment”, Comptes Rendus Mathematique, 348:5-6 (2010), 301  crossref
    13. M. S. Sgibnev, “On the existence of a solution of a homogeneous system of generalized Wiener–Hopf equations”, Izv. Math., 74:3 (2010), 595–606  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. A. F. Voronin, “A method for determining the partial indices of symmetric matrix functions”, Siberian Math. J., 52:1 (2011), 41–53  mathnet  crossref  mathscinet  isi
    15. Przemysław Klusik, Zbigniew Palmowski, “A Note on Wiener–Hopf Factorization for Markov Additive Processes”, J Theor Probab, 2012  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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