Extremes of multidimensional Gaussian processes

This paper considers extreme values attained by a centered, multidimensional Gaussian process X(t)=(X1(t),...,Xn(t)) minus drift d(t)=(d1(t),...,dn(t)), on an arbitrary set T. Under mild regularity conditions, we establish the asymptotics of for positive thresholds qi>0, i=1,...,n and u-->[infinity]. Our findings generalize and extend previously known results for the single-dimensional and two-dimensional cases. A number of examples illustrate the theory.