Dȩbicki, Krzysztof and Liu, Peng and Michna, Zbigniew (2020) Sojourn Times of Gaussian Processes with Trend. Journal of Theoretical Probability, 33 (4). pp. 2119-2166. DOI https://doi.org/10.1007/s10959-019-00934-9
Dȩbicki, Krzysztof and Liu, Peng and Michna, Zbigniew (2020) Sojourn Times of Gaussian Processes with Trend. Journal of Theoretical Probability, 33 (4). pp. 2119-2166. DOI https://doi.org/10.1007/s10959-019-00934-9
Dȩbicki, Krzysztof and Liu, Peng and Michna, Zbigniew (2020) Sojourn Times of Gaussian Processes with Trend. Journal of Theoretical Probability, 33 (4). pp. 2119-2166. DOI https://doi.org/10.1007/s10959-019-00934-9
Abstract
We derive exact tail asymptotics of sojourn time above the level u≥ 0 P(v(u)∫0TI(X(t)-ct>u)dt>x),x≥0,as u→ ∞, where X is a Gaussian process with continuous sample paths, c is some constant, v(u) is a positive function of u and T∈ (0 , ∞]. Additionally, we analyze asymptotic distributional properties of τu(x):=inf{t≥0:v(u)∫0tI(X(s)-cs>u)ds>x},x≥0,as u→ ∞, where inf ∅ = ∞. The findings of this contribution are illustrated by a detailed analysis of a class of Gaussian processes with stationary increments and a family of self-similar Gaussian processes.
Item Type: | Article |
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Uncontrolled Keywords: | Cumulative Parisian ruin time; Exact asymptotics; First passage time; Gaussian process with stationary increments; Generalized Berman-type constant; Self-similar Gaussian process; Sojourn; occupation times |
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: | 04 Dec 2020 17:11 |
Last Modified: | 30 Oct 2024 19:14 |
URI: | http://repository.essex.ac.uk/id/eprint/28174 |
Available files
Filename: sojourns_revision.pdf