Extremes of Chi-square Processes with Trend

Peng Liu; Lanpeng Ji

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arXiv · 1407.6501

Extremes of Chi-square Processes with Trend

Peng Liu·Lanpeng Ji

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Abstract

This paper studies the supremum of a chi-square process with trend over a threshold-dependent-time horizon. Under the assumption that the chi-square process is generated from a centered self-similar Gaussian process and the trend function is modeled by a polynomial function, we obtain the exact tail asymptotics of the supremum of the chi-square process with trend. These results are of interest in applications in engineering, insurance, queueing and statistics, etc. Some possible extensions of our results are also discussed.

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Peng Liu, Lanpeng Ji. 2015-02-23. Extremes of Chi-square Processes with Trend. https://arxiv.org/abs/1407.6501

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