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Izvestiya: Mathematics, 2006, Volume 70, Issue 2, Pages 363–383
DOI: https://doi.org/10.1070/IM2006v070n02ABEH002315 (Mi im562) 		 
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
English version PDF (378 kB) Citations (1)
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DOI: https://doi.org/10.1070/IM2006v070n02ABEH002315
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.
Received: 19.05.2005
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2006, Volume 70, Issue 2, Pages 159–178
DOI: https://doi.org/10.4213/im562
Bibliographic databases:
UDC: 517.962.28, 519.218.24
MSC: 15A03, 15A24, 32A38, 46E27, 46H05, 60J80, 60K05
Language: English
Original paper language: Russian
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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  • https://doi.org/10.1070/IM2006v070n02ABEH002315
  • https://www.mathnet.ru/eng/im/v70/i2/p159
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:304
    Russian version PDF:199
    English version PDF:10
    References:44
    First page:2
     
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