Let (Xn) be a strictly stationary random sequence and Mn=max{X1,...,Xn}. Suppose that some of the random variables X1,X2,... can be observed and denote by the maximum of observed random variables from the set {X1,...,Xn}. We determine the limiting distribution of random vector under some...

Let ξ(t) be a standard stationary Gaussian process with covariance function r(t), and η(t), another smooth random process. We consider the probabilities of exceedances of ξ(t)η(t) above a high level u occurring in an interval [0,T] with T0. We present asymptotically exact results for...

The maximum MT of the storage process Y(t)=sups[greater-or-equal, slanted]t(X(s)-X(t)-c(s-t)) in the interval [0,T] is dealt with, in particular, for growing interval length T. Here X(s) is a fractional Brownian motion with Hurst parameter, 0<H<1. For fixed T the asymptotic behaviour of MT was analysed by Piterbarg (Extremes 4(2) (2001) 147) by determining an approximation for the probability P MT>u for u--[infinity]. Using this expression the...</h<1.>

For certain Gaussian processes X(t) with trend -ct[beta] and variance V2(t), the ruin time is analyzed where the ruin time is defined as the first time point t such that X(t)-ct[beta]=u. The ruin time is of interest in finance and actuarial subjects. But the ruin time is also of interest in...