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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