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Sojourn Times of Gaussian Processes with Trend

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. ISSN 0894-9840

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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
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 > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 04 Dec 2020 17:11
Last Modified: 18 Aug 2022 10:40
URI: http://repository.essex.ac.uk/id/eprint/28174

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