First excess levels of vector processes. (1994)

• Record Type: Journal Article
• Authors: Dshalalow, Jewgeni H.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 7:Number 3(1994)
• Page Start: 457
• Page End: 464
• Publication Date: 1994
• Subjects: fluctuations -- two-dimensional marked renewal process -- first-passage time -- first excess level -- termination index -- queueing -- quorum -- vacations -- N-policy -- T-policy; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953394000365
• Languages: English
• ISSNs: 1048-9533

Abstract

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.