The distributions of interrecord fillings

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.