International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1994 / Article

Open Access

Volume 7 |Article ID 762639 | 8 pages | https://doi.org/10.1155/S1048953394000365

First excess levels of vector processes

Received01 Apr 1994
Revised01 Aug 1994

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.

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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