Abstract: This paper studies the supremum of chi-square processes with trend over a threshold-dependent-time horizon. Under the assumptions 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.

2000 AMS Mathematics Subject Classification: Primary: 60G15; Secondary: 60G70.

Keywords and phrases: Chi-square process, Gaussian random field, safety region, tail asymptotics, first passage time, Pickands constant, Piterbarg constant, Fernique-type inequality.