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Mat. Sb., 2006, Volume 197, Number 3, Pages 69–86 (Mi msb1538)  

This article is cited in 8 scientific papers (total in 8 papers)

The matrix analogue of the Blackwell renewal theorem on the real line

M. S. Sgibnev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: The full analogue of Blackwell's theorem is proved for a matrix renewal measure on the whole real line, both in the non-lattice and in the lattice cases. A complete result on a decomposition of Stone type for a matrix renewal measure is obtained. Asymptotic properties of solutions of systems of integral equations of renewal type on the real line are established.
Bibliography: 21 titles.

DOI: https://doi.org/10.4213/sm1538

Full text: PDF file (519 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2006, 197:3, 369–386

Bibliographic databases:

UDC: 517.962.28
MSC: Primary 60K05; Secondary 45M05
Received: 22.03.2005

Citation: M. S. Sgibnev, “The matrix analogue of the Blackwell renewal theorem on the real line”, Mat. Sb., 197:3 (2006), 69–86; Sb. Math., 197:3 (2006), 369–386

Citation in format AMSBIB
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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. 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
    2. M. S. Sgibnev, “The uniqueness of a solution to the renewal type system of integral equations on the line”, Siberian Math. J., 51:1 (2010), 168–173  mathnet  crossref  mathscinet  isi  elib  elib
    3. 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
    4. Kim Jeongsim, Kim Bara, “Asymptotics in the $MAP/G/1$ queue with critical load”, Stoch. Anal. Appl., 28:1 (2010), 157–168  crossref  mathscinet  zmath  isi  elib  scopus
    5. Bae Yun Han, Kim Bara, Choi Bong Dae, Kim Jeongsim, “Tail asymptotic behavior of resequencing buffer content for selective-repeat ARQ”, Oper. Res. Lett., 39:4 (2011), 272–277  crossref  mathscinet  zmath  isi  elib  scopus
    6. Predrag R. Jelenković, Mariana Olvera-Cravioto, “Implicit renewal theorem for trees with general weights”, Stochastic Processes and their Applications, 2012  crossref  mathscinet  isi  scopus
    7. Kim J., Kim B., Kim H.-S., “G/M/1 Type Structure of a Risk Model with General Claim Sizes in a Markovian Environment”, J. Ind. Manag. Optim., 8:4 (2012), 909–924  crossref  mathscinet  zmath  isi  elib  scopus
    8. Kh. A. Khachatryan, “O razreshimosti odnoi sistemy nelineinykh integralnykh uravnenii tipa Gammershteina na pryamoi”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 19:2 (2019), 164–181  mathnet  crossref  elib
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