Abstract
Normal comparison lemma and Slepian’s inequality are essential tools for the analysis of extremes of Gaussian processes. In this paper we show that the Normal comparison lemma for Gaussian vectors can be extended to order statistics of Gaussian arrays. Our applications include the derivation of mixed Gumbel limit laws for the order statistics of stationary Gaussian processes and the investigation of lower tail behavior of order statistics of self-similar Gaussian processes.
| Original language | English |
|---|---|
| Pages (from-to) | 93-116 |
| Number of pages | 24 |
| Journal | Alea (Rio de Janeiro) |
| Volume | 14 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2017 |
| Externally published | Yes |
Keywords
- Normal comparison inequality
- Slepian’s inequality
- conjunction probability
- lower tail probability
- mixed Gumbel limit theorem
- order statistics process
- self-similar Gaussian process