Asymptotics of~the~generalized renewal functions when the~variance is~finite
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 632-637
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We study the asymptotic behavior, as $t \to\infty$, of the generalized renewal functions $$ \Phi_n(t)=\sum_{k=0}^\infty\frac{n\cdot(n+k-1)!}{k!}\mathsf{P}\{S_k\le t\}, $$
where $n>0$ is an integer and $S_{k}$ are partial sums of a sequence of independent identically distributed random variables with positive mean and finite variance.
Keywords:
generalized renewal functions, higher renewal moments, random walk, ladder epochs.
@article{TVP_1997_42_3_a15,
author = {M. S. Sgibnev},
title = {Asymptotics of~the~generalized renewal functions when the~variance is~finite},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {632--637},
publisher = {mathdoc},
volume = {42},
number = {3},
year = {1997},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a15/}
}
M. S. Sgibnev. Asymptotics of~the~generalized renewal functions when the~variance is~finite. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 632-637. http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a15/