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...

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 deal with the distribution of the first zero Rn of the real part of the empirical characteristic function related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, several cases have to be considered. For most of the...

Any multivariate distribution can occur as the limit of extreme values in a sequence of independent, non-identically distributed random vectors. Under a reasonable uniform negligibility condition the class of such limit distribution can be totally characterized, which extends the known...

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...

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...

Let {Xk, k[epsilon]Z} be a stationary Gaussian sequence with EX1 - 0, EX2k = 1 and EX0Xk = rk. Define [tau]x = inf{k: Xk - [beta]k} the first crossing point of the Gaussian sequence with the function - [beta]t ([beta] 0). We consider limit distributions of [tau]x as [beta]--0, depending on the...