Ukrainian Mathematical Journal

, Volume 40, Issue 6, pp 588–592

Estimates for the deviations of the transition characteristics of nonhomogeneous markov processes

  • V. V. Anisimov
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    R. L. Dobrushin, “Central limit theorem for nonhomogeneous Markov chains. I; II,” Teor. Veroyatn. Primen.,1, No. 1, 72–89 (1956); No. 4, 365–425 (1956).Google Scholar
  2. 2.
    M. Loeve, Probability Theory, Van Nostrand, Princeton (1963).Google Scholar
  3. 3.
    P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).Google Scholar
  4. 4.
    V. V. Anisimov and M. F. Taurov, “Estimates for the rapprochement of the transition characteristics of Markov chains,” in: Abstracts of Reports. Fourth Internat. Conf. on Probability Theory and Mathematical Statistics, Vol. 1 (1985), pp. 28–29.Google Scholar
  5. 5.
    V. V. Anisimov, Limit Theorems for Random Processes and Their Application to Discrete Summation Schemes [in Russian], Vishcha Shkola, Kiev (1976).Google Scholar
  6. 6.
    V. V. Anisimov, Asymptotic Methods in the Analysis of Stochastic Systems [in Russian], Metsniereba, Tbilisi (1984).Google Scholar
  7. 7.
    V. V. Anisimov, “Limit theorems for nonhomogeneous weakly dependent summation schemes,” Teor. Veroyatn. Mat. Statist., No. 27, 10–22 (1982).Google Scholar
  8. 8.
    V. S. Korolyuk, “On the asymptotic behavior of the occupation time of a semi-Markov process in a subset of states,” Ukr. Mat. Zh.,21, No. 6, 842–845 (1969).Google Scholar
  9. 9.
    V. S. Korolyuk and A. F. Turbin, Semi-Markov Processes and Their Applications [in Russian], Naukova Dumka, Kiev (1976).Google Scholar
  10. 10.
    A. M. Zubkov, “Inequalities for restricted transition probabilities and their applications,” Mat. Sb.,109 (151), No. 4, 491–532 (1979).Google Scholar
  11. 11.
    A. D. Solov'ev, “Analytic Methods for the computation and the estimation of reliability,” in: Problems in the Mathematical Theory of Reliability [in Russian], Radio i Svyaz', Moscow (1983), pp. 9–112.Google Scholar
  12. 12.
    I. N. Kovalenko, The Analysis of Rare Events at the Estimation of System Efficiency [in Russian], Sov. Radio, Moscow (1980).Google Scholar
  13. 13.
    D. J. Aldous, “Markov chains with almost exponential hitting times,” Stochastic Process. Appl.,13, No. 3, 305–310 (1982).Google Scholar
  14. 14.
    N. V. Kartashov, “Estimates of the geometrical asymptotic behavior of first exit times,” Teor. Veroyatn. Primen.,30, No. 1, 202–203 (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • V. V. Anisimov
    • 1
  1. 1.Kiev UniversityUSSR

Personalised recommendations