Geodesic
The distributions of interrecord fillings
Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 56-73

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In a sequence of independent positive random variables with the same continuous distribution function a monotonic subsequence of record values is chosen. A corresponding sequence of record times divides the initial sequence into interrecord intervals. Let $\alpha_i^j \ (i\geqslant 1, \,j = 1, \ldots , i)$ be the number of random variables in the interval between $i$-th and $(i+1)$-th record moments with values between $(j-1)$-th and $j$-th records. Explicit formulas for the joint distributions of the random variables $\alpha_i^j,\,1\leqslant j\leqslant i\leqslant n$, are derived, limit theorems for the distributions of $\alpha_i^j$ for $i-j\to\infty$ are proved.
Keywords: independent random variables, records, record moments, explicit formulas for distributions, limit theorems. 
@article{DM_2015_27_3_a4,
     author = {O. P. Orlov and N. Yu. Pasynkov},
     title = {The distributions of interrecord fillings},
     journal = {Diskretnaya Matematika},
     pages = {56--73},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_3_a4/}
}
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O. P. Orlov; N. Yu. Pasynkov. The distributions of interrecord fillings. Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 56-73. http://geodesic.mathdoc.fr/item/DM_2015_27_3_a4/