On the Bounds for a Two-Dimensional Birth-Death Process with Catastrophes

The model of a two-dimensional birth-death process with possible catastrophes is studied. The upper bounds on the rate of convergence in some weighted norms and the corresponding perturbation bounds are obtained. In addition, we consider the detailed description of two examples with 1-periodic inten...

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Veröffentlicht in:	Mathematics (Basel) 2018-05, Vol.6 (5), p.80
Hauptverfasser:	Sinitcina, Anna, Satin, Yacov, Zeifman, Alexander, Shilova, Galina, Sipin, Alexander, Kiseleva, Ksenia, Panfilova, Tatyana, Kryukova, Anastasia, Gudkova, Irina, Fokicheva, Elena
Format:	Artikel
Sprache:	eng
Schlagworte:	birth-death process bounds catastrophes continuous-time Markov chains Convergence Death Food science Markov processes Norms Queuing theory rate of convergence Two dimensional models Upper bounds
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Beschreibung
Zusammenfassung:	The model of a two-dimensional birth-death process with possible catastrophes is studied. The upper bounds on the rate of convergence in some weighted norms and the corresponding perturbation bounds are obtained. In addition, we consider the detailed description of two examples with 1-periodic intensities and various types of death (service) rates. The bounds on the rate of convergence and the behavior of the corresponding mathematical expectations are obtained for each example.
ISSN:	2227-7390 2227-7390
DOI:	10.3390/math6050080