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Theory of Probability and Mathematical Statistics

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On the distribution of storage processes from the class $ V(\varphi,\psi)$


Authors: R. E. Yamnenko and O. S. Shramko
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal: Theor. Probability and Math. Statist. 83 (2011), 191-206
MSC (2010): Primary 60G07; Secondary 60K25
DOI: https://doi.org/10.1090/S0094-9000-2012-00851-X
Published electronically: February 2, 2012
MathSciNet review: 2768858
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Abstract | References | Similar Articles | Additional Information

Abstract: Estimates for the distribution of a storage process

$\displaystyle Q(t)=\sup _{s\le t}\big (X(t)-X(s)-(f(t)-f(s))\big )$

are obtained in the paper, where $ (X(t),t\in T)$ is a stochastic process belonging to the class $ V(\varphi ,\psi )$ and where the service output rate $ f(t)$ is a continuous function. In particular, the results hold if $ (X(t),t\in T)$ is a Gaussian process. Several examples of applications of the results obtained in the paper are given for sub-Gaussian stationary stochastic processes.

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Additional Information

R. E. Yamnenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: yamnenko@univ.kiev.ua

O. S. Shramko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: shes21@ukr.net

DOI: https://doi.org/10.1090/S0094-9000-2012-00851-X
Keywords: Metric entropy, queue, storage process, estimate of a distribution, sub-Gaussian process
Received by editor(s): April 21, 2010
Published electronically: February 2, 2012
Article copyright: © Copyright 2012 American Mathematical Society