Ji, L orcid.org/0000-0002-7790-7765 and Peng, X (2022) Extrema of multi-dimensional Gaussian processes over random intervals. Journal of Applied Probability, 59 (1). pp. 81-104. ISSN 0021-9002
Abstract
This paper studies the joint tail asymptotics of extrema of the multi-dimensional Gaussian process over random intervals defined as
P(u) := P{∩ni=1(supt∈[0,Ti](Xi(t)+cit) > aiu)} , u→∞ , where Xi(t) , t ≥ 0 , i=1,2,…,n , are independent centered Gaussian processes with stationary increments, T=(T1,…,Tn) is a regularly varying random vector with positive components, which is independent of the Gaussian processes, and ci ∈ R , ai > 0 , i = 1,2,…,n . Our result shows that the structure of the asymptotics of P(u) is determined by the signs of the drifts ci . We also discuss a relevant multi-dimensional regenerative model and derive the corresponding ruin probability.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust.This article has been published in a revised form in https://doi.org/10.1017/jpr.2021.37. This version is free to view and download for private research and study only. Not for re-distribution or re-use. |
Keywords: | Joint tail asymptotic; Gaussian process; perturbed random walk; ruin probability; fluid model; fractional Brownian motion; regenerative model |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 12 Apr 2021 10:55 |
Last Modified: | 13 Apr 2023 01:19 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/jpr.2021.37 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:172988 |