Boundary Crossing Probabilities of Poisson Counting Processes with General Boundaries

by Lehmann, Axel


Preprint series: 98-07, Preprints

The paper is published: Kahle, W.; v. Collani, E.; Franz, J.; Jensen, U. (ed.): Advances in Stochastic Models for Reliability, Quality and Safety, Birkhäuser,Boston-Basel-Berlin 1998, 153-166)

60G40 Stopping times; optimal stopping problems; gambling theory, See also {62L15, 90D60}
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

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