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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/8547

Title: Exit problems for the difference of a compound Poisson process and a compound renewal process
Authors: Kadankov, Victor
Issue Date: 2008
Publisher: SPRINGER
Citation: QUEUEING SYSTEMS, 59(3-4). p. 271-296
Abstract: In this paper we solve a two-sided exit problem for a difference of a compound Poisson process and a compound renewal process. More specifically, we determine the Laplace transforms of the joint distribution of the first exit time, the value of the overshoot and the value of a linear component at this time instant. The results obtained are applied to solve the two-sided exit problem for a particular class of stochastic processes, i.e. the difference of the compound Poisson process and the renewal process whose jumps are exponentially distributed. The advantage is that these results are in a closed form, in terms of resolvent sequences of the process. We determine the Laplace transforms of the busy period of the systems M-x vertical bar G(delta)vertical bar 1 vertical bar B, G(delta)
vertical bar 1 vertical bar B in case when delta similar to exp(lambda). Additionally, we prove the weak convergence of the two-boundary characteristics of the process to the corresponding functionals of the standard Wiener process.
Notes: [Kadankova, Tetyana] Hasselt Univ, Ctr Stat, B-3590 Diepenbeek, Belgium. [Kadankov, Victor] Ukrainian Natl Acad Sci 3, Inst Math, Kiev 4, Ukraine.
URI: http://hdl.handle.net/1942/8547
DOI: 10.1007/s11134-008-9084-7
ISI #: 000259483800004
ISSN: 0257-0130
Category: A1
Type: Journal Contribution
Validation: ecoom, 2009
Appears in Collections: Research publications

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