Large Deviations for the Boundary Crossing Probabilities of Some Random Fields

For Y_1,Y_2,…i.i.d.with Y_1～N(μ,1) and S_n=sum from 1 to n(Y_i),the large deviations are obtained for the probabilities that conditionally given (i) S_m=0, and (ii) S_(m_i)=Applied these results to the double change-points model with some nuisance parameters, we developed the large deviation for the significance level of the likelihood ratio test.