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Some renewal-type theorems. (Russian) Zbl 0623.60106
The authors study the asymptotic behaviour of \(f*H_ n(x)\) as n,x\(\to \infty\), where \(\{H_ n(x)\}\) is a sequence of renewal functions corresponding to the sequence \(\{G_ n(x)\}\) of complex-valued functions and \(f\geq 0\) is an arbitrary monotone, bounded and integrable function. \(G_ n(x)\) are supposed to be close to a probability distribution function, which is non-latticed and has positive and finite first moment.
Reviewer: L.Mutafchiev

MSC:
60K05 Renewal theory
30E15 Asymptotic representations in the complex plane
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