This article is cited 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.

UDC: 517.962.28, 519.218.24

MSC: 15A03, 15A24, 32A38, 46E27, 46H05, 60J80, 60K05

Received: 19.05.2005

DOI: 10.4213/im562

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

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