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

Extremes of locally stationary chi-square processes with trend