Geodesic
On the joint limiting distribution of sums and maxima of stationary normal sequences
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 4, pp. 817-820

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Let $X_1,X_2,\dots$ be a stationary sequence of standard normal random variables. Let $\rho_n=\mathbf{E}(X_1 X_{n+1})$. Ho and Hsing derived the asymptotic joint distribution of $\sum_{i=1}^n X_i$ and $\max_{1\le i\le n}X_i$ for the case $\rho_n\log n\to\gamma\in[0,\infty)$. In this paper we extend this result for the case where $\rho_n$ is convex with $\rho_n=o(1)$, and $(\rho_n\log n)^{-1}$ is monotone with $(\rho_n\log n)^{-1}=o(1)$.
Keywords: asymptotic distribution, stationary normal sequence, sum.
Mots-clés : maxima 
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     author = {Z. Peng and S. Nadarajah},
     title = {On the joint limiting distribution of sums and maxima of stationary normal sequences},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {817--820},
     publisher = {mathdoc},
     volume = {47},
     number = {4},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_4_a16/}
}
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Z. Peng; S. Nadarajah. On the joint limiting distribution of sums and maxima of stationary normal sequences. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 4, pp. 817-820. http://geodesic.mathdoc.fr/item/TVP_2002_47_4_a16/