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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 2, Pages 159–178 (Mi izv562)  

This article is cited in 1 scientific paper (total in 1 paper)

Exact asymptotic expansions for solutions of multi-dimensional renewal equations

M. S. Sgibnev

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

Abstract: We derive expansions with exact asymptotic expressions for the remainders for solutions of multi-dimensional renewal equations. The effect of the roots of the characteristic equation on the asymptotic representation of solutions is taken into account. The resulting formulae are used to investigate the asymptotic behaviour of the average number of particles in age-dependent branching processes having several types of particles.

DOI: https://doi.org/10.4213/im562

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English version:
Izvestiya: Mathematics, 2006, 70:2, 363–383

Bibliographic databases:

UDC: 517.962.28, 519.218.24
MSC: 15A03, 15A24, 32A38, 46E27, 46H05, 60J80, 60K05
Received: 19.05.2005

Citation: M. S. Sgibnev, “Exact asymptotic expansions for solutions of multi-dimensional renewal equations”, Izv. RAN. Ser. Mat., 70:2 (2006), 159–178; Izv. Math., 70:2 (2006), 363–383

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Hadji E.M., Kambo N.S., Rangan A., “Two-Dimensional Renewal Function Approximation”, Commun. Stat.-Theory Methods, 44:15 (2015), 3107–3124  crossref  mathscinet  zmath  isi  elib  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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