PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 58(72), pp. 143148 (1995) 

On the asymptotic behaviour of two sequences related by a convolution equationEdward OmeyEHSAL, Stormstrat 2, 1000 Brussels, BelgiumAbstract: We analyse analyse the relation between the asymptotic behaviour of two sequences $\{a(n)\}$ and $\{b(n)\}$ related by the system of equations $nb(n) = a\ast b(n)$, where $\ast$ denotes convolution. This type of relation appears in studying discrete infinitely divisible laws and more recently in risk theory. In Hawkes and Jenkins (1978) the authors considered this relation and obtained the asymptotic behaviour of $b(n)$ in the cases where $a(n)\to\alpha$, or $\frac 1n\sum_{k=0}^na(k)\to \alpha$, where $\alpha>0$. We consider the case $\alpha = 0$ and consider Oanalogues. Classification (MSC2000): 40A99, 40E99 Full text of the article:
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