We derive the exact asymptotic behavior of the ruin probability P{X(t)x for some t0} for the process , with respect to level x which tends to infinity. We assume that the underlying process [xi](t) is a.s. continuous stationary Gaussian with mean zero and correlation function regularly varying...

In this paper multivariate extensions of the Friedman and Page tests for the comparison of several treatments are introduced. Related unadjusted and adjusted treatment effect estimates for the multivariate response variable are also found and their properties discussed. The test statistics and...

For a particular sequence of Gaussian processes we consider the maximum Mn(T) up to time T and its limiting behaviour as T=T(n) and n converges to [infinity]. This sequence occurs in the approximation of the path of the continuous Gaussian process by broken lines. This limiting behaviour was...

We consider the multivariate Farlie-Gumbel-Morgenstern class of distributions and discuss their properties with respect to the extreme values. This class was used to consider dependence in multivariate distributions and their ordering. We show that the extreme values of these distributions...

We consider the extreme values of fractional Brownian motions, self-similar Gaussian processes and more general Gaussian processes which have a trend -ct[beta] for some constants c,[beta]0 and a variance t2H. We derive the tail behaviour of these extremes and show that they occur mainly in the...

For i.i.d. bivariate normal vectors we consider the maxima of the projections with respect to two arbitrary directions. A limit theorem for these maxima is proved for the case that the angle of the two directions approaches zero. The result is generalized to a functional limit theorem.

It is known that the partial maximum of nonstationary Gaussian sequences converges in distribution and that the number of exceedances of a boundary is asymptotically a Poisson random variable, under certain restrictions. We investigate the rate of Poisson approximation for the number of...

We consider general nonstationary max-autoregressive sequences Xi, i [greater-or-equal, slanted] 1, with Xi = Zimax(Xi - 1, Yi) where Yi, i [greater-or-equal, slanted] 1 is a sequence of i.i.d. random variables and Zi, i [greater-or-equal, slanted] 1 is a sequence of independent random variables...