Journal of Applied Mathematics and Stochastic Analysis
Volume 7 (1994), Issue 3, Pages 457-464
doi:10.1155/S1048953394000365
Abstract
This paper analyzes the behavior of a point process marked by a two-dimensional renewal process with dependent components about some fixed (two-dimensional) level. The compound process evolves until one of its marks hits (i.e.
reaches or exceeds) its associated level for the first time. The author targets a
joint transformation of the first excess level, first passage time, and the index of
the point process which labels the first passage time. The cases when both marks
are either discrete or continuous or mixed are treated. For each of them, an explicit and compact formula is derived. Various applications to stochastic models are
discussed.