Extremes of vector-valued Gaussian processes with Trend
Abstract
Let X(t)=(X1(t), …, Xn(t)), t∈ T⊂ R be a centered vector-valued Gaussian process with independent components and continuous trajectories, and h(t)=(h1(t),…, hn(t)), t∈ T be a vector-valued continuous function. We investigate the asymptotics of P(t∈ T 1≤ i≤ n(Xi(t)+hi(t))>u) as u∞. As an illustration to the derived results we analyze two important classes of X(t): with locally-stationary structure and with varying variances of the coordinates, and calculate exact asymptotics of simultaneous ruin probability and ruin time in a Gaussian risk model.
0