Extremes of Chi-square Processes with Trend
  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. 
Peng Liu and Lanpeng Ji
math.PR