Let $\{N(t), t \geq 0\}$ be the renewal process associated to an i.i.d. sequence $X_1, X_2, \ldots$ of nonnegative interarrival times having finite moment generating function near the origin. In this article we give strong and weak limiting laws for the maximal and minimal increments $\sup_{0 \leq t \leq T - K}(N(t + K) - N(t))$ and $\inf_{0 \leq t \leq T - k}(N(t + K) - N(t))$, where $K = K_T$ is a function of $T$ such that $0 \leq K_T \leq T$.
Publié le : 1989-04-14
Classification:
Renewal processes,
laws of large numbers,
weak laws,
law of the iterated logarithm,
invariance principles,
60F15,
60F05,
60F17,
60G55
@article{1176991422,
author = {Deheuvels, Paul and Steinebach, Josef},
title = {Sharp Rates for Increments of Renewal Processes},
journal = {Ann. Probab.},
volume = {17},
number = {4},
year = {1989},
pages = { 700-722},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991422}
}
Deheuvels, Paul; Steinebach, Josef. Sharp Rates for Increments of Renewal Processes. Ann. Probab., Tome 17 (1989) no. 4, pp. 700-722. http://gdmltest.u-ga.fr/item/1176991422/