First excess levels of vector processes
type: Item
instance of: scholarly article
title: First excess levels of vector processes
zbMATH Open document ID: 0812.60077
DOI: 10.1155/S1048953394000365
author: Jewgeni H. Dshalalow
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1995-05-14T00:00:00Z
full work available at URL: https://eudml.org/doc/47149
review text: Summary: 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.
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60K15
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 722525
zbMATH Keywords: fluctuations
zbMATH Keywords: first-passage time
zbMATH Keywords: first excess level
zbMATH Keywords: termination index
zbMATH Keywords: stochastic models
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 722525