Zurück zu den Preprints des Jahres 1998


1998-07

Boundary Crossing Probabilities of Poisson Counting Processes with General Boundaries

by Lehmann, Axel.


Series: 1998-07, Preprints

MSC:
60G40 Stopping times; optimal stopping problems; gambling theory
60J75 Jump processes

Abstract:
This paper gives exact boundary crossing probabilities for finite time
intervals associated with
Poisson processes and general moving boundaries in both one and two
boundary cases. These probabilities are relevant in various applications
of sequential stopping in statistics, reliability analysis, risk
theory, dam engineering, etc. We deal with both homogeneous and
nonhomogeneous Poisson processes as well as mixed Poisson processes
where the Pólya-Lundberg process is considered in detail.

Keywords:
Poisson processes, Pólya-Lundberg process, first passage time, general boundaries, stopping time, sequential analysis

This paper was published in:
Kahle, W.; v. Collani, E.; Franz, J.; Jensen, U. (ed.): Advances in Stochastic Models for Reliability, Quality and Safety, Birkhäuser,Bos