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Generalized birth-death processes and their application to the ageing models

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Abstract

The generalized birth-death processes were introduced to model ageing of objects of different nature. The results obtained were compared with the model based on the conventional birth-death processes.

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References

  1. Lisniansky, A. and Levitin, G., Multi-State System Reliability Assessment, Singapore: World Scientific, 2003.

    Google Scholar 

  2. Dimitrov, B., Rykov, V., and Stanchev, P., On Multi-state Reliability Systems, Proc. MMR-2002, Trondheim, June 17–21, 2002.

  3. Rykov, V. and Dimitrov, B., On Multi-state Reliability Systems, in Proc. Int. Seminar, Petrozavodsk, September 8–13, 2002, pp. 128–135 (see also http://www.jip.ru/2002-2-2-2002.htm).

  4. Rykov, V., Dimitrov, B., Green, D., Jr., and Stanchev, P., Reliability of Complex Hierarchical Systems with Fault Tolerance Units, in Proc. MMR-2004, Santa Fe, June, 2004 (Published on CD).

  5. Dimitrov, B., Green, D., Rykov, V., and Stanchev, P., Reliability Model for Biological Objects. Longevity, Ageing and Degradation Models, Trans. First Russian-French Conf. (LAD-2004), St. Petersburg, June 7–9, 2004, Antonov, V., Huber, C., Nikulin, M., and Polischook, V., Eds., St. Petersburg: S.-Peterburg. Gos. Polytechnical Univ., 2004, vol. 2, pp. 230–240.

    Google Scholar 

  6. Rykov, V. and Efrosinin, D., Reliability Control of Fault Tolerance Units, in Abstracts 4 Int. Conf. Math. Methods Reliability (MMR-2004), Santa Fe, 21–25 July, 2004 (Published on CD).

  7. Rykov, V. and Efrosinin, D., Reliability Control of Biological Systems with Failures Longevity, Aging and Degradation Models, Trans. First Russian-French Conf. (LAD-2004), St. Petersburg, June 7–9, 2004, Antonov, V., Huber, C., Nikulin, M., and Polischook, V., Eds., St. Petersburg: S.-Peterburg. Gos. Polytechnical Univ., 2004, vol. 2, pp. 241–255.

    Google Scholar 

  8. Rykov, V. and Buldaeva, E., On Reliability Control of Fault Tolerance Units: Regenerative Approach, Trans. XXIV Int. Seminar Stab. Probl. Stochast. Modes, September 10–17, 2004, Jurmala: Transport and Telecommunication Inst., 2004.

    Google Scholar 

  9. van Doorn, E.A., Quasi-stationary Distributions and Convergence to Quasi-stationarity of Birth-Death Processes, Adv. Appl. Prob., 1991, vol. 26, no. 4, pp. 683–700.

    Google Scholar 

  10. Kijima, M., Nair, M.G., Pollet, P.K., and van Doorn, E.A., Limiting Conditional Distributions for Birth-Death Processes, Adv. Appl. Prob., 1997, vol. 29, no. 1, pp. 185–204.

    Google Scholar 

  11. Karlin, S. and McGregor, J.L., The Differential Equations of Birth-and-Death Processes, and the Stieltjes Moment Problem, Trans. Am. Math. Soc., 1957, vol. 85, pp. 489–546.

    MathSciNet  Google Scholar 

  12. Granovsky, B.L. and Zeifman, A., Nonstationary Queues: Estimation of the Rate of Convergence, Queuing Sys., 2004, vol. 46, no. 3–4, pp. 363–388.

    MathSciNet  Google Scholar 

  13. Korolyuk, V.S. and Turbin, A.F., Polumarkovskie protsessy i ikh prilozheniya (Semi-Markov Processes and Their Applications), Kiev: Naukova Dumka, 1976.

    Google Scholar 

  14. McDonald, D., On Semi-Markov and Semi-regenerative Processes. I, II, Z. Wahrch. Verw. Geb., 1978, vol. 42, no. 2, pp. 261–377; Ann. Prob., 1978, vol. 6, no. 6, pp. 995–1014.

    MATH  MathSciNet  Google Scholar 

  15. Jacod, J., Théorèms de renouvellement et classification pour les chaines semi-Markoviennes, Ann. Inst. Henri Poincaré, 1971, sect. B. 7, no. 2, pp. 83–129.

  16. Petrovskii, I.G., Lektsii po teorii obyknovennykh differentsial’nykh uravnenii (Lectures on the Theory of Ordinary Differential Equations), Moscow: GITTL, 1952.

    Google Scholar 

  17. Feller, W., An Introduction to Probability Theory and Its Applications, New York: Wiley, 1957. Translated under the title Vvedenie v teoriyu veroyatnostei i ee prilozheniya, Moscow: Mir, 1967, vol. 2.

    Google Scholar 

  18. Lavrent’ev, M.A. and Shabat, B.V., Metody teorii funktsii kompleksnogo peremennogo (Methods of the Theory of Functions of Complex Variables), Moscow: Fizmatgiz, 1958.

    Google Scholar 

  19. Korolyuk, V.S. and Turbin, A.F., Fazovoe ukrupnenie slozhnykh sistem (Phase Agglomeration of Complex Systems), Kiev: Vishcha Shkola, 1978.

    Google Scholar 

  20. Korolyuk, V.S. and Korolyuk, V.V., Stochastic Models of Systems, New York: Kluwer, 1999.

    Google Scholar 

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Authors and Affiliations

  1. Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    V. V. Rykov

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  1. V. V. Rykov
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Additional information

Original Russian Text © V.V. Rykov, 2006, published in Automatika i Telemekhanika, 2006, No. 3, pp. 103–120.

This work was supported by the Russian Foundation for Basic Research, project no. 04-07-90115.

This paper was recommended for publication by V.M. Vishnevskii, a member of the Editorial Board

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Rykov, V.V. Generalized birth-death processes and their application to the ageing models. Autom Remote Control 67, 435–451 (2006). https://doi.org/10.1134/S0005117906030088

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  • DOI: https://doi.org/10.1134/S0005117906030088

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