Remainder Term Estimates of the Renewal Function

Carlsson, Hasse

Ann. Probab., Tome 11 (1983) no. 4, p. 143-157 / Harvested from Project Euclid

Résumé

Let $\mu$ be a probability measure and $H(x) = \sum^\infty_{n=0} \mu^{n_\ast}(-\infty, x\rbrack$ its renewal function. It is well-known that $H(x) - x/\mu_1 - \mu_2/2\mu^2_1 \rightarrow 0$ as $x \rightarrow +\infty$ if $\mu_1 > 0$ and $\mu$ is a nonlattice measure. ($\mu_k$ is the $k$th moment of $\mu$.) The rate of this convergence is studied under further conditions on $\mu$.

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Publié le : 1983-02-14
Classification:  Renewal theory,  renewal function,  60K05