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|Title: ||Exit problems for the difference of a compound Poisson process and a compound renewal process|
|Authors: ||Kadankov, Victor|
|Issue Date: ||2008|
|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.|
|ISI #: ||000259483800004|
|Type: ||Journal Contribution|
|Validation: ||ecoom, 2009|
|Appears in Collections: ||Research publications|
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