Geodesic
Asymptotics of the $k$th record times
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 925-928

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Let $\eta_{0,n}\le\eta_{1,n}\le\dots\le\eta_{n,n}$ be the set of ordered statistics constructed by a sequence of independent identically distributed random variables $\eta_0,\eta_1,\dots,\eta_n$ and let $\nu^{(k)}(0)=k-1$, $$ \nu^{(k)}(n+1)=\min\{j>\nu^{(k)}(n):\eta_j>\eta_{j-k,j-1}\}, \qquad n=0,1,2,\dots, $$ be the $k$th record times. For fixed $k$ and $n$, the asymptotic behavior of the probability $\mathbf P\{\nu^{(k)}(n)>t\}$ is studied as $t\to\infty$.
Keywords: the set of ordered statistics, record times, kth record times. 
@article{TVP_1995_40_4_a21,
     author = {A. L. Yakymiv},
     title = {Asymptotics of the $k$th record times},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {925--928},
     publisher = {mathdoc},
     volume = {40},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a21/}
}
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A. L. Yakymiv. Asymptotics of the $k$th record times. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 925-928. http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a21/