Abstract
Some fields of research initiated by I. N. Kovalenko and used in joint articles with the author are reviewed. These are: method of artificial regeneration points, asymptotic insensitivity, Monte Carlo method, variance reduction methods, principle of monotone failures.
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References
E. Nummelin, A Splitting Technique for φ-Recurrent Markov Chains, Inst. Math., Helsinki Univ. Technol. Espoo, Helsinki (1976).
A. A. Borovkov, “Ergodicity and stability theorems for a class of stochastic equations and their applications,” Teor. Veroyatn. Primenen., 23, Issue 2, 241–262 (1978).
K. B. Athreya and P. E. Ney, “A new approach to the limit theory of recurrent Markov chains,” Trans. Amer. Math. Soc., 245, No. 1, 493–501 (1978).
V. S. Korolyuk and A. F. Turbin, Markov Renewal Processes in System Reliability Problems [in Russian], Naukova Dumka, Kyiv (1982).
I. N. Kovalenko, “Limiting theorems of reliability theory,” Kibernetika, No. 6, 106–116 (1977).
I. N. Kovalenko and N. Yu. Kuznetsov, Generating an Embedded Renewal Process for Essentially Multidimensional Processes in Queueing Theory and its Application to Formulating Limiting Theorems [in Russian], Prepr. No. 80–12, Inst. of Cybern. Acad. Sci. Ukr., Kyiv (1980).
I. N. Kovalenko and N. Yu. Kuznetsov, “Renewal process and rare events limit theorems for essentially multidimensional queueing processes,” Math. Operationsforsch. und Statist., 12, No. 2, 211–224 (1981).
V. M. Zolotarev, “Continuity of stochastic sequences generated by recurrent procedures,” Teor. Veroyatn. Primenen., 20, Issue 4, 834–847 (1975).
A. A. Borovkov, “Ergodicity and stability theorems for a class of stochastic equations and their applications,” Teor. Veroyatn. Primenen., 23, Issue 2, 241–262 (1978).
V. V. Kalashnikov, Qualitative Analysis of the Behavior of Complex Systems by the Method of Trial Functions [in Russian], Nauka, Moscow (1978).
I. N. Kovalenko, “Calculating corrections to queueing system characteristics,” in: Proc. Semin. on Stability of Stochastic Models [in Russian], VNIISI, Moscow (1986), pp. 45–48.
I. N. Kovalenko and N. Yu. Kuznetsov, Methods to Design Highly Reliable Systems [in Russian], Radio I Svyaz’, Moscow (1988).
I. N. Kovalenko and N. Yu. Kuznetsov, “Analysis of the deviation of the nonstationary availability factor of a restorable system from its stationary value,” Cybern. Syst. Analysis, 35, No. 2, 79–92 (1999).
I. N. Kovalenko, N. Yu. Kuznetsov, and A. N. Nakonechnyi, “Optimization of reliability characteristics of systems based on quantitative estimates of continuity and accelerated simulation,” in: Proc. Semin. on Stability of Stochastic Models [in Russian], VNIISI, Moscow (1988), pp. 79–84.
Yu. M. Ermol’ev, Stochastic Simulation Methods [in Russian], Nauka, Moscow (1976).
I. N. Kovalenko and N. Yu. Kuznetsov, “Asymptotic insensitivity of queuing systems,” in: P. Franken, D. König, U. Arndt, and V. Schmidt, Queues and Point Processes, John Wiley & Sons, Chichester, New York (1981).
I. N. Kovalenko, J. B., Atkinson, and K. V. Mykhalevych, “Three cases of light traffic insensitivity of the loss probability in a GI/G/m/0 loss system to the shape of the service time distribution,” Queueing Systems, 45, No. 3, 245–271 (2003).
J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods, Methuen, London (1964).
N. P. Buslenko, Modeling of Complex Systems [in Russian], Nauka, Moscow (1978).
I. N. Kovalenko, “Some issues of the theory of reliability of complex systems,” in: Cybernetics in the Service of Communism [in Russian], 2, Energiya, Moscow (1964), pp. 194–205.
I. N. Kovalenko “Asymptotic method to estimate the reliability of complex systems in: On the Reliability of Complex Systems [in Russian], Sov. Radio, Moscow (1966), pp. 205–223.
I. N. Kovalenko “Calculating characteristics of highly reliable systems by an analytic statistical method,” Elektron. Modelirovanie, 2, No. 4, 5–8 (1980).
I. N. Kovalenko and N. Yu. Kuznetsov, “Accelerated simulation methods for characteristics of highly reliable systems,” in: Statistics and Control of Random Processes [in Russian], Nauka, Moscow (1989), pp. 77–86.
I. N. Kovalenko, V. G. Krivutsa, and N. Yu. Kuznetsov, “Test of the practical application of statistical modeling methods in reliability theory,” Cybernetics, 23, No. 5, 707–714 (1987).
I. N. Kovalenko, N. Yu. Kuznetsov, and V. G. Krivutsa, “Statistical-simulation method (Monte Carlo method),” in: Reliability and Efficiency in Engineering [in Russian], 2, Mashinostroenie, Moscow (1987), pp. 208–250.
I. N. Kovalenko, N. Yu. Kuznetsov, and Ph. A. Pegg, Mathematical Theory of Reliability of Time Dependent Systems with Practical Applications, Wiley, Chichester (1997).
I. N. Kovalenko, “Reliability analysis of complex systems,” Voprosy Radioelektroniki, 12, No. 9, 50–68 (1965).
A. D. Solov’ev, “Asymptotic behavior of the moment of the first rare event in a regenerative process,” Izv. AN SSSR, Tekhn. Kibernetika, No. 6, 79–89 (1971).
D. B. Gnedenko and A. D. Solov’ev, “Reliability analysis of complex renewable systems,” Izv. AN SSSR, Tekhn. Kibernetika, No. 3, 121–128 (1975).
I. N. Kovalenko, “Estimation of the intensity of the flow of nonmonotone refusals in the queuing system (≤ λ)/G/m,” Ukr. Math. J., 52, No. 9, 1396–1402 (2000).
I. N. Kovalenko and N. Yu. Kuznetsov, “Principle of monotonic failures and its application to the reliability analysis of structurally complex systems,” in: Stochastic Models of Systems [in Russian], Voen. Akad. PVO i Sukhoputn Voisk, Kyiv (1986), pp. 25–45.
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Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 101–108, May–June 2010.
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Kuznetsov, N.Y. On some fields of research initiated by academician I. N. Kovalenko. Cybern Syst Anal 46, 436–442 (2010). https://doi.org/10.1007/s10559-010-9218-x
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DOI: https://doi.org/10.1007/s10559-010-9218-x