Abstract
The paper studies the behavior of an (l+3)th-dimensional, delayed renewal process with dependent components, the first three (called active) of
which are to cross one of their respective thresholds. More specifically, the
crossing takes place when at least one of the active components reaches or
exceeds its assigned level. The values of the other two active components,
as well as the rest of the components (passive), are to be registered. The
analysis yields the joint functional of the “crossing level” and other
characteristics (some of which can be interpreted as the first passage time)
in a closed form, refining earlier results of the author. A brief, informal discussion of various applications to stochastic models is presented.