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Theory of Probability and Mathematical Statistics

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Versions of a compound Poisson process

Author: D. V. Gusak
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 27-38
MSC (2000): Primary 60G50, 60J70; Secondary 60K10, 60K15
Published electronically: February 7, 2005
MathSciNet review: 2110902
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider two versions of an oscillating compound Poisson process with reflections from two boundaries. The versions are constructed from an upper continuous compound Poisson process $\xi(t)$ and two functionals of it, namely the exit time from an interval and first upcrossing or downcrossing times from the upper or lower boundaries, respectively. The basic characteristics of the processes considered in the paper are given in terms of the potential and resolvent of the process $\xi(t)$ introduced earlier by V. S. Korolyuk.

References [Enhancements On Off] (What's this?)

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Additional Information

D. V. Gusak
Affiliation: Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs’ka Street 3, Kyiv 4, Ukraine

Keywords: Compound Poisson process, resolvent and potential functions, first exit time from an interval, moment generating function of the exit time, reflections of a Poisson process from two boundaries, versions of the risk process
Received by editor(s): September 16, 2002
Published electronically: February 7, 2005
Article copyright: © Copyright 2005 American Mathematical Society