Asymptotic Distribution of Maxima Multivariate Locally Stationary Gaussian Processes

Let \(X_1(t),\cdots,X_p(t)),0\leq t\leq T\ be p dimensional locally stationary Gaussian processes with asymptotically centered mean m_k(t), k=1,\cdots,p and constant variance. M_k(T)=\sup\X_k(t),0\leq t\leq T\, k=1,\cdots,p. Under some conditions, the asymptotic distribution of M(T)=(M_1(T),\cdots,M_p(T)) as T\rightarrow\infty is obtained.