A Conditioned Limit Law Result for Jumps in the Sequence of Partial Maxima of a Stationary Gaussian Sequence.
William P. McCormick · 1982
Conditional of a jump occurring, the limiting distribution for the size of the jump in the partial maxima sequence for a class of stationary Gaussian sequences is derived. It is shown that the limiting distribution is exponential with mean square root of (1-gamma) where gamma equals the atom at zero of the spectral distribution function associated with the correlation function of the sequence. A generalization of this result to include the entire jump sequence subsequent to the jump conditioned to occur is also presented.