多维局部平稳高斯过程最大值的联合渐近分布
Asymptotic Distribution of Maxima Multivariate Locally Stationary Gaussian Processes
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摘要: \(X_1(t),\cdots,X_p(t)),0\leq t\leq T\为p维局部平稳高斯过程, 具有渐近中心化的均值m_k(t)和常数的方差, M_k(T)=\sup\X_k(t),0\leq t\leq T\,\;k=1,\cdots,p, 当T\rightarrow\infty时, 本文在一定条件下获得了M(T)=(M_1(T),\cdots,M_p(T))的联合渐近分布.Abstract: 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.
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