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Theory of Probability and Mathematical Statistics

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Exit, passage, and crossing times and overshoots for a Poisson compound process with an exponential component


Author: T. Kadankova
Translated by: O. I. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 75 (2006).
Journal: Theor. Probability and Math. Statist. 75 (2007), 23-39
MSC (2000): Primary 60J05, 60J10; Secondary 60J45
DOI: https://doi.org/10.1090/S0094-9000-08-00711-4
Published electronically: January 23, 2008
MathSciNet review: 2321178
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Abstract | References | Similar Articles | Additional Information

Abstract: Integral transforms of the joint distribution of the first exit time from an interval and the overshoot over the boundary at the exit time are found for a Poisson process with an exponentially distributed negative component. We obtain the distributions of the following functionals of the process on an exponentially distributed time interval: the supremum, infimum, and the value of the process, numbers of upcrossings and downcrossings, the number of passages into an interval and overshoots over a boundary of an interval.


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Additional Information

T. Kadankova
Affiliation: Center for Statistics, Hasselt University, Agoralaan, 3590 Diepenbeek, Belgium
Email: tetyana.kadankova@uhasselt.be

DOI: https://doi.org/10.1090/S0094-9000-08-00711-4
Keywords: Poisson process with an exponentially distributed negative component, one-boundary functionals of a process, exit times from an interval, overshoot over a boundary, supremum and infimum of the process, crossing times for an interval
Received by editor(s): September 6, 2005
Published electronically: January 23, 2008
Article copyright: © Copyright 2008 American Mathematical Society

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