Geodesic
Conditional distributions of the times of one-sided sequential approximations
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 2, pp. 364-366

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Let $X_1,X_2,\dots$ be a sequence of independent random variables with common continuous distribution function $F(x)$. Let $a$ be an arbitrary point of the support of the underlying probability measure. The present paper deals with random indices of those $X$ which approach point $a$ from the left. Conditional distributions of such random variables are investigated and some limit laws for them are formulated.
Keywords: moments and values of one-sided sequential approximations, record moments and record values, limit theorems. 
@article{TVP_2002_47_2_a12,
     author = {A. V. Stepanov},
     title = {Conditional distributions of the times of one-sided sequential approximations},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {364--366},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_2_a12/}
}
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A. V. Stepanov. Conditional distributions of the times of one-sided sequential approximations. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 2, pp. 364-366. http://geodesic.mathdoc.fr/item/TVP_2002_47_2_a12/