Document Type
Article
Publication Title
Journal of Applied Mathematics and Stochastic Analysis
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.
DOI
10.1155/S1048953394000365
Publication Date
1994
Recommended Citation
Dshalalow, J. (1994). First excess levels of vector processes. Journal of Applied Mathematics and Stochastic Analysis, 7(3), 457.