We develop a strong approximation approach to extended multidimensional renewal theory. The consequences of this approximation are a Bahadur-Kiefer type representation of the renewal process in terms of partial sums, Strassen and Chung type laws of the iterated logarithm. We also give a characterization of the renewal process by four classes of deterministic curves in the sense of Revesz (1982). We generalize our results to the case of non-independent and/or nonidentically distributed random vectors.
Publié le : 1984-11-14
Classification:
Renewal process,
Wiener process,
strong approximation,
laws of the iterated logarithm,
60F17,
60K05
@article{1176993145,
author = {Horvath, Lajos},
title = {Strong Approximation of Extended Renewal Processes},
journal = {Ann. Probab.},
volume = {12},
number = {4},
year = {1984},
pages = { 1149-1166},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993145}
}
Horvath, Lajos. Strong Approximation of Extended Renewal Processes. Ann. Probab., Tome 12 (1984) no. 4, pp. 1149-1166. http://gdmltest.u-ga.fr/item/1176993145/