EXTREMES OF CHI-SQUARE PROCESSES WITH TREND
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.