Let $\{Z_k, -\infty < k < \infty\}$ be iid where the $Z_k$'s have regularly varying tail probabilities. Under mild conditions on a real sequence $\{c_j, j \geq 0\}$ the stationary process $\{X_n: = \sum^\infty_{j=0} c_jZ_{n-j}, n \geq 1\}$ exists. A point process based on $\{X_n\}$ converges weakly and from this, a host of weak limit results for functionals of $\{X_n\}$ ensue. We study sums, extremes, excedences and first passages as well as behavior of sample covariance functions.
Publié le : 1985-02-14
Classification:
Extreme values,
stable laws,
regular variation,
moving average,
point processes,
60F05,
60F17,
60G55,
62M10
@article{1176993074,
author = {Davis, Richard and Resnick, Sidney},
title = {Limit Theory for Moving Averages of Random Variables with Regularly Varying Tail Probabilities},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 179-195},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993074}
}
Davis, Richard; Resnick, Sidney. Limit Theory for Moving Averages of Random Variables with Regularly Varying Tail Probabilities. Ann. Probab., Tome 13 (1985) no. 4, pp. 179-195. http://gdmltest.u-ga.fr/item/1176993074/