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Absorption and first-passage times for a compound Poisson process in a general upper boundary

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

S. F. L. Gallot
S. F. L. Gallot*
Affiliation:
DSIR Physical Sciences
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Abstract

This paper considers the absorption of a non-decreasing compound Poisson process of finite order in a general upper boundary. The problem is relevant in fields such as risk theory, Kolmogorov–Smirnov statistics and sequential analysis. The probability of absorption and first-passage times are given in terms of a generating function which depends on the boundary only and can be computed readily. Absorption is certain or not as the asymptotic slope of the boundary is greater or less than the expected increase of the process in unit time. The case of the linear boundary is considered in detail.

Keywords

ABSORPTION PROBABILITYPASSAGE TIMESPOISSON PROCESS

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60J75: Jump processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 4 , December 1993 , pp. 835 - 850
Copyright
Copyright © Applied Probability Trust 1993 

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