An Upper Bound for the Renewal Function

Stone, Charles J.

Ann. Math. Statist., Tome 43 (1972) no. 6, p. 2050-2052 / Harvested from Project Euclid

Résumé

In this note we show that the renewal function $H$ corresponding to a random walk with positive mean $\mu$ and finite variance $\sigma^2$ satisfies the inequality $H(x) < \mu^{-1} x + 3(1 + \mu^{-2}\sigma^2)$.

Publié le : 1972-12-14
Classification:

@article{1177690883,
     author = {Stone, Charles J.},
     title = {An Upper Bound for the Renewal Function},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 2050-2052},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177690883}
}

Stone, Charles J. An Upper Bound for the Renewal Function. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  2050-2052. http://gdmltest.u-ga.fr/item/1177690883/