ON THE DISTRIBUTION OF FUNCTIONALS OF STATIONARY GAUSSIAN-PROCESSES

Let (X(t), 0 less-than-or-equal-to t less-than-or-equal-to 1) be a zero mean, continuous-path stationary Gaussian process with autocovariance function rho(X)(S) - 1 - kappa Absolute value of s, where 0 less-than-or-equal-to kappa less-than-or-equal-to 2. We investigate the joint distribution of the maximum and the minimum of X on [0, tau] and the distribution of the range of X on [0, tau] for 0 < T less-than-or-equal-to 1.