On Piterbarg Max-Discretisation Theorem for Standardised Maximum of Stationary Gaussian Processes

Zhongquan Tan and Enkelejd Hashorva ()
Additional contact information
Zhongquan Tan: Jiaxing University
Enkelejd Hashorva: University of Lausanne

Methodology and Computing in Applied Probability, 2014, vol. 16, issue 1, 169-185

Abstract: Abstract With motivation from Hüsler (Extremes 7:179–190, 2004) and Piterbarg (Extremes 7:161–177, 2004) in this paper we derive the joint limiting distribution of standardised maximum of a continuous, stationary Gaussian process and the standardised maximum of this process sampled at discrete time points. We prove that these two random sequences are asymptotically complete dependent if the grid of the discrete time points is sufficiently dense, and asymptotically independent if the grid is sufficiently sparse. We show that our results are relevant for computational problems related to discrete time approximation of the continuous time maximum.

Keywords: Extreme values; Piterbarg max-discretisation theorem; Studentised maxima; Piterbarg inequality; Approximation of random processes; Primary 60F05; Secondary 60G15 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-012-9305-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:16:y:2014:i:1:d:10.1007_s11009-012-9305-8

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-012-9305-8

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().