Ergodicity and perturbation bounds for inhomogeneous birth and death processes with additional transitions from and to the origin

Alexander Zeifman; Anna Korotysheva; Yacov Satin; Victor Korolev; Sergey Shorgin; Rostislav Razumchik

International Journal of Applied Mathematics and Computer Science (2015)

  • Volume: 25, Issue: 4, page 787-802
  • ISSN: 1641-876X

Abstract

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Service life of many real-life systems cannot be considered infinite, and thus the systems will be eventually stopped or will break down. Some of them may be re-launched after possible maintenance under likely new initial conditions. In such systems, which are often modelled by birth and death processes, the assumption of stationarity may be too strong and performance characteristics obtained under this assumption may not make much sense. In such circumstances, timedependent analysis is more meaningful. In this paper, transient analysis of one class of Markov processes defined on non-negative integers, specifically, inhomogeneous birth and death processes allowing special transitions from and to the origin, is carried out. Whenever the process is at the origin, transition can occur to any state, not necessarily a neighbouring one. Being in any other state, besides ordinary transitions to neighbouring states, a transition to the origin can occur. All possible transition intensities are assumed to be non-random functions of time and may depend (except for transition to the origin) on the process state. To the best of our knowledge, first ergodicity and perturbation bounds for this class of processes are obtained. Extensive numerical results are also provided.

How to cite

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Alexander Zeifman, et al. "Ergodicity and perturbation bounds for inhomogeneous birth and death processes with additional transitions from and to the origin." International Journal of Applied Mathematics and Computer Science 25.4 (2015): 787-802. <http://eudml.org/doc/275957>.

@article{AlexanderZeifman2015,
abstract = {Service life of many real-life systems cannot be considered infinite, and thus the systems will be eventually stopped or will break down. Some of them may be re-launched after possible maintenance under likely new initial conditions. In such systems, which are often modelled by birth and death processes, the assumption of stationarity may be too strong and performance characteristics obtained under this assumption may not make much sense. In such circumstances, timedependent analysis is more meaningful. In this paper, transient analysis of one class of Markov processes defined on non-negative integers, specifically, inhomogeneous birth and death processes allowing special transitions from and to the origin, is carried out. Whenever the process is at the origin, transition can occur to any state, not necessarily a neighbouring one. Being in any other state, besides ordinary transitions to neighbouring states, a transition to the origin can occur. All possible transition intensities are assumed to be non-random functions of time and may depend (except for transition to the origin) on the process state. To the best of our knowledge, first ergodicity and perturbation bounds for this class of processes are obtained. Extensive numerical results are also provided.},
author = {Alexander Zeifman, Anna Korotysheva, Yacov Satin, Victor Korolev, Sergey Shorgin, Rostislav Razumchik},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {inhomogeneous birth and death processes; ergodicity bounds; perturbation bounds},
language = {eng},
number = {4},
pages = {787-802},
title = {Ergodicity and perturbation bounds for inhomogeneous birth and death processes with additional transitions from and to the origin},
url = {http://eudml.org/doc/275957},
volume = {25},
year = {2015},
}

TY - JOUR
AU - Alexander Zeifman
AU - Anna Korotysheva
AU - Yacov Satin
AU - Victor Korolev
AU - Sergey Shorgin
AU - Rostislav Razumchik
TI - Ergodicity and perturbation bounds for inhomogeneous birth and death processes with additional transitions from and to the origin
JO - International Journal of Applied Mathematics and Computer Science
PY - 2015
VL - 25
IS - 4
SP - 787
EP - 802
AB - Service life of many real-life systems cannot be considered infinite, and thus the systems will be eventually stopped or will break down. Some of them may be re-launched after possible maintenance under likely new initial conditions. In such systems, which are often modelled by birth and death processes, the assumption of stationarity may be too strong and performance characteristics obtained under this assumption may not make much sense. In such circumstances, timedependent analysis is more meaningful. In this paper, transient analysis of one class of Markov processes defined on non-negative integers, specifically, inhomogeneous birth and death processes allowing special transitions from and to the origin, is carried out. Whenever the process is at the origin, transition can occur to any state, not necessarily a neighbouring one. Being in any other state, besides ordinary transitions to neighbouring states, a transition to the origin can occur. All possible transition intensities are assumed to be non-random functions of time and may depend (except for transition to the origin) on the process state. To the best of our knowledge, first ergodicity and perturbation bounds for this class of processes are obtained. Extensive numerical results are also provided.
LA - eng
KW - inhomogeneous birth and death processes; ergodicity bounds; perturbation bounds
UR - http://eudml.org/doc/275957
ER -

References

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