Stability estimates of generalized geometric sums and their applications

Evgueni I. Gordienko

Kybernetika (2004)

  • Volume: 40, Issue: 2, page [257]-272
  • ISSN: 0023-5954

Abstract

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The upper bounds of the uniform distance ρ ∑ k = 1 ν X k , ∑ k = 1 ν X ˜ k between two sums of a random number ν of independent random variables are given. The application of these bounds is illustrated by stability (continuity) estimating in models in queueing and risk theory.

How to cite

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Gordienko, Evgueni I.. "Stability estimates of generalized geometric sums and their applications." Kybernetika 40.2 (2004): [257]-272. <http://eudml.org/doc/33698>.

@article{Gordienko2004,
abstract = {The upper bounds of the uniform distance $\rho \left(\sum ^\nu _\{k=1\}X_k,\sum ^\nu _\{k=1\}\tilde\{X\}_k\right)$ between two sums of a random number $\nu $ of independent random variables are given. The application of these bounds is illustrated by stability (continuity) estimating in models in queueing and risk theory.},
author = {Gordienko, Evgueni I.},
journal = {Kybernetika},
keywords = {geometric sum; upper bound for the uniform distance; stability; risk process; ruin probability; geometric sum; upper bound for the uniform distance; stability; risk process; ruin probability},
language = {eng},
number = {2},
pages = {[257]-272},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Stability estimates of generalized geometric sums and their applications},
url = {http://eudml.org/doc/33698},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Gordienko, Evgueni I.
TI - Stability estimates of generalized geometric sums and their applications
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 2
SP - [257]
EP - 272
AB - The upper bounds of the uniform distance $\rho \left(\sum ^\nu _{k=1}X_k,\sum ^\nu _{k=1}\tilde{X}_k\right)$ between two sums of a random number $\nu $ of independent random variables are given. The application of these bounds is illustrated by stability (continuity) estimating in models in queueing and risk theory.
LA - eng
KW - geometric sum; upper bound for the uniform distance; stability; risk process; ruin probability; geometric sum; upper bound for the uniform distance; stability; risk process; ruin probability
UR - http://eudml.org/doc/33698
ER -

References

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  10. Kalashnikov V. V., Geometric Sums: Bounds for Rare Events with Applications, Kluwer, Dordrecht 1997 Zbl0881.60043MR1471479
  11. Kalashnikov V. V., Rachev S. T., Mathematical Methods for Construction of Queueing Models, Wadsworth & Brooks/Cole, Pacific Grove 1990 Zbl0709.60096MR1052651
  12. Petrov V. V., Sums of Independent Random Variables, Springer–Verlag, Berlin 197 MR0388499
  13. Rachev S. T., Probability Metrics and the Stability of Stochastic Models, Wiley, Chichester 1991 Zbl0744.60004MR1105086
  14. Senatov V. V., Normal Approximation: New Results, Methods and Problems, VSP, Utrecht 1998 Zbl0926.60005MR1686374
  15. Ushakov V. G., Ushakov V. G., Some inequalities for characteristic functions with bounded variation, Moscow Univ. Comput. Math. Cybernet. 3 (2001), 45–52 
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