Geodesic
Exact asymptotic expansions for solutions of multi-dimensional
Izvestiya. Mathematics , Tome 70 (2006) no. 2, pp. 363-383.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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M. S. Sgibnev. Exact asymptotic expansions for solutions of multi-dimensional. Izvestiya. Mathematics , Tome 70 (2006) no. 2, pp. 363-383. http://geodesic.mathdoc.fr/item/IM2_2006_70_2_a5/

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