极值理论、遍历理论与平稳稳定过程短记忆与长记忆之边界
概率论
2007-05-23 v1
摘要
我们研究平稳 \alpha-稳定过程的偏最大值。我们将它们的渐近行为与流的遍历理论性质相联系。我们观察到偏最大值序列的渐近行为在流从耗散变为保守时发生急剧变化，并论证这可能指示了从短记忆过程到长记忆过程的转变。
引用
@article{arxiv.math/0410149,
title = {Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes},
author = {Gennady Samorodnitsky},
journal= {arXiv preprint arXiv:math/0410149},
year = {2007}
}
备注
Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000261