Short Communications

Conditional distributions of the times of one-sided sequential approximations

A. V. Stepanov

Kaliningrad State Technical University

Abstract: 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.

Received: 26.03.1999

DOI: 10.4213/tvp3656

 English version: Theory of Probability and its Applications, 2003, 47:2, 363–365

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