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http://hdl.handle.net/1942/10329
Title: | Intersections of an Interval By a Difference of a Compound Poisson Process and a Compound Renewal Process | Authors: | Kadankov, V. KADANKOVA, Tetyana VERAVERBEKE, Noel |
Issue Date: | 2009 | Publisher: | TAYLOR & FRANCIS INC | Source: | STOCHASTIC MODELS, 25(2). p. 270-300 | Abstract: | In this article we determine the Laplace transforms of the one-boundary characteristics and the distribution of the number of intersections of a fixed interval by a difference of a compound Poisson process and a compound renewal process. The results obtained are applied for a particular case of this process, namely, for the difference of the compound Poisson process and the renewal process whose jumps are geometrically distributed. The advantage is that these results are in a closed form, in terms of resolvent sequences of the process. In this case, under certain assumptions, we find the limit distributions of the one-boundary and two-boundary characteristics of the process. In addition, we prove the weak convergence of these distributions to the corresponding distributions of a symmetric Wiener process. | Notes: | [Kadankov, V.] Natl Acad Sci Ukraine, Inst Math, UA-01601 Kiev 4, Ukraine. [Kadankova, T.; Veraverbeke, N.] Hasselt Univ, Ctr Stat, Diepenbeek, Belgium. | Keywords: | Difference of compound renewal processes; First exit time; Intersections of an interval; Linear component; Resolvent sequence; Value of the overshoot | Document URI: | http://hdl.handle.net/1942/10329 | Link to publication/dataset: | http://dx.doi.org:10.1080/15326340902869978 | ISSN: | 1532-6349 | e-ISSN: | 1532-4214 | DOI: | 10.1080/15326340902869978 | ISI #: | 000265869000004 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2010 |
Appears in Collections: | Research publications |
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Intersections of an interval.pdf | Peer-reviewed author version | 281.79 kB | Adobe PDF | View/Open |
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