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

Author:
T. Kadankova

Translated by:
O. I. Klesov

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

Full-text PDF Free Access

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

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