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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
##### Keywords:
convolution; asymptotic behaviour; renewal functions