HIGH EXCURSIONS FOR NONSTATIONARY GENERALIZED CHI-SQUARE PROCESSES

Suppose that X(t), t is an element of[0,T], is a centered differentiab le Gaussian random process, X(1)(t),...,X(n)(t) are independent copies of X(t). An exact asymptotic behavior of large deviation probabilitie s for the process chi(b)(2)(t)=Sigma(i=1)(n)b(i)(2)X(i)(2)(t), where b (1),b(2),...,b(n) are positive constants is investigated. It is assume d that the variance of the process attains its global maximum in only one inner point of the interval [0,T], with a nondegeneracy condition.