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Theory of Probability and Mathematical Statistics

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Storage impulsive processes on increasing time intervals

Authors: V. S. Koroliuk, R. Manca and G. D’Amico
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 89 (2013).
Journal: Theor. Probability and Math. Statist. 89 (2014), 71-81
MSC (2010): Primary 60J45; Secondary 60K05
Published electronically: January 26, 2015
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Abstract | References | Similar Articles | Additional Information

Abstract: A storage impulsive process $ S(t)$ is a sum of (jointly independent) random variables defined on the embedded Markov chain of a homogeneous Markov process.

A storage impulsive process is considered in the scheme of series on increasing time intervals $ t/\varepsilon $, with a small parameter $ \varepsilon \to 0$, $ \varepsilon >0$. A storage impulsive process is investigated in the average and diffusion approximation scheme. The large deviation problem is considered under a corresponding scaling with an asymptotically small diffusion.

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

  • 1. Vladimir S. Koroliuk and Nikolaos Limnios, Stochastic systems in merging phase space, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. MR 2205562
  • 2. Jin Feng and Thomas G. Kurtz, Large deviations for stochastic processes, Mathematical Surveys and Monographs, vol. 131, American Mathematical Society, Providence, RI, 2006. MR 2260560
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Additional Information

V. S. Koroliuk
Address at time of publication: Institute of Mathematics, Kyiv, Ukraine

R. Manca
Affiliation: University of Rome “La Sapienza”, Italy

G. D’Amico
Affiliation: Universita’di Chieti, Chieti, Italy

Keywords: Storage impulsive process; average, diffusion approximation; large deviation problem
Received by editor(s): October 20, 2012
Published electronically: January 26, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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