Extremes of locally stationary chi-square processes with trend

Chi-square processes with trend appear naturally as limiting processes in various statistical models. In this paper we are concerned with the exact tail asymptotics of the supremum taken over (0; 1) of a class of locally stationary chi-square processes with particular admissible trends. An important tool for establishing our results is a weak version of Slepian's lemma for chi-square processes. Some special cases including squared Brownian bridge and Bessel process are discussed.