an:04011616
Zbl 0623.60106
Kostawa, B. A.; Shurenkov, V. M.
Some renewal-type theorems
RU
Teor. Veroyatn. Primen. 32, No. 1, 105-113 (1987).
00166340
1987
j
60K05 30E15
convolution; asymptotic behaviour; renewal functions
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.
L.Mutafchiev