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Exit, passage, and crossing times and overshoots for a Poisson compound process with an exponential component
Author(s):
T.
Kadankova
Translated by:
O. I. Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 75
(2006).
Journal:
Theor. Probability and Math. Statist.
No. 75
(2007),
23-39.
MSC (2000):
Primary 60J05, 60J10;
Secondary 60J45
Posted:
January 23, 2008
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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:
10.1090/S0094-9000-08-00711-4
PII:
S 0094-9000(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):
6/SEP/2005
Posted:
January 23, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
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