Another Upper Bound for the Renewal Function
Daley, D. J.
Ann. Probab., Tome 4 (1976) no. 6, p. 109-114 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
The general renewal equation and real variable methods are used to show that for a renewal process with generic lifetime random variable $X \geqq 0$ having distribution $F$ and finite first and second moments $EX = \lambda^{-1}$ and $EX^2$, the renewal function $U(x) = \sum^\infty_0 F^{n^\ast(x)$ satisfies $U(x) \leqq \lambda x_+ + C\lambda^2EX^2$ for a certain constant $C$ independent of $F$. Stone (1972) showed that $1 \leqq C \leqq 2.847 \cdots$; it is proved here that $C \leqq 1.3186 \cdots$ and conjectured that $C = 1$.
Publié le : 1976-02-14
Classification:  Renewal function,  bound,  60K05 
@article{1176996188,
     author = {Daley, D. J.},
     title = {Another Upper Bound for the Renewal Function},
     journal = {Ann. Probab.},
     volume = {4},
     number = {6},
     year = {1976},
     pages = { 109-114},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996188}
}

Daley, D. J. Another Upper Bound for the Renewal Function. Ann. Probab., Tome 4 (1976) no. 6, pp.  109-114. http://gdmltest.u-ga.fr/item/1176996188/