Debicki, Krzysztof and Hashorva, Enkelejd and Liu, Peng and Michna, Zbigniew (2023) Sojourn times of Gaussian random fields. ALEA : Latin American Journal of Probability and Mathematical Statistics, 20 (1). pp. 249-289. DOI https://doi.org/10.30757/ALEA.v20-10
Debicki, Krzysztof and Hashorva, Enkelejd and Liu, Peng and Michna, Zbigniew (2023) Sojourn times of Gaussian random fields. ALEA : Latin American Journal of Probability and Mathematical Statistics, 20 (1). pp. 249-289. DOI https://doi.org/10.30757/ALEA.v20-10
Debicki, Krzysztof and Hashorva, Enkelejd and Liu, Peng and Michna, Zbigniew (2023) Sojourn times of Gaussian random fields. ALEA : Latin American Journal of Probability and Mathematical Statistics, 20 (1). pp. 249-289. DOI https://doi.org/10.30757/ALEA.v20-10
Abstract
This paper is concerned with the asymptotic analysis of sojourn times of random fields with continuous sample paths. Under a very general framework we show that there is an interesting relationship between tail asymptotics of sojourn times and that of supremum. Moreover, we establish the uniform double-sum method to derive the tail asymptotics of sojourn times. In the literature, based on the pioneering research of S. Berman the sojourn times have been utilised to derive the tail asymptotics of supremum of Gaussian processes. In this paper we show that the opposite direction is even more fruitful, namely knowing the asymptotics of supremum of random processes and fields (in particular Gaussian) it is possible to establish the asymptotics of their sojourn times. We illustrate our findings considering i) two dimensional Gaussian random fields, ii) chi-process generated by stationary Gaussian processes and iii) stationary Gaussian queueing processes.
Item Type: | Article |
---|---|
Uncontrolled Keywords: | Sojourn times; occupation times; exact asymptotics; generalized Berman-type constants; Gaussian random fields; chi-process; queueing process |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 28 Feb 2023 12:11 |
Last Modified: | 16 May 2024 21:34 |
URI: | http://repository.essex.ac.uk/id/eprint/33927 |
Available files
Filename: sojournfield_fin.pdf
Filename: 20-10.pdf