Some renewal-type theorems. (Russian) Zbl 0623.60106

Kostawa, B. A.; Shurenkov, V. M.

Teor. Veroyatn. Primen. 32, No. 1, 105-113 (1987).

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