Approximation of some stochastic models

  • V. V. Kalashnikov


Approximation problems are of great importance in applied mathematics. The approximation itself consists in changing the initial mathematical model to another one which is more preferable to consider (e.g. from a computational point of view). At most the arising problems are implied by the problem of receiving quantitative estimates of the approximation accuracy.


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  1. Anichkin, S.A. (1983). Hyper-Erlang approximation of probability distributions on (0,∞) and its application. Stability problems for stochastic models. Lect.Notes in Math, 1982, 1–16.MathSciNetCrossRefGoogle Scholar
  2. Anichkin, S.A. and V.V. Kalashnikov (1981). Continuity of random sequences and approximation of Markov chains. Adv.Appl.Prob., 13, 402–414.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Kalashnikov, V.V. (1978a). Qualitative analysis of the behaviour of complex systems by trial functions (in Russian), Nauka, Moscow.Google Scholar
  4. Kalashnikov, V.V. (1978b). Solution of the approximation problem for a denumerable Markov chain. Engineering Cybernetics, v.16, N 3.Google Scholar
  5. Kalashnikov, V.V. (1981a). Estimations of convergence rate and stability for regenerative and renovative processes. Colloquia Math.Soc.J.Bolyai. 24. Point Processes and Queueing Problems, Keszthely (Hungary), 1978, 163–180. North-Holland, Amsterdam.Google Scholar
  6. Kalashnikov, V.V. (1981b). Methods of continuity estimates for states enlarging problem. Stability problems for stochastic models, 48–53, (in Russian) VNIISI, Moscow.Google Scholar
  7. Kalashnikov, V.V. (1983a). Continuity estimates for queueing models and related problems. The 4-th International summer school on probability theory and math.statistics, Varna, 1982, 120–165 (in Russian). Publ.House of the Bulgarian Acad.Sci., Sofia.Google Scholar
  8. Kalashnikov, V.V. (1983b). The analysis of continuity of queueing systems. Probability Theory and Math.Stat., Lee. Notes in Math., 1021, 268–278. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo.Google Scholar
  9. Kalashnikov, V.V. (1983c). An estimate of convergence rate in Renyi’s theorem. Stability problems for stochastic models, 48–57 (in Russian), VNIISI, Moscow.CrossRefGoogle Scholar
  10. Kalashnikov, V.V. and S.Yu. Vsehsviatski (1985). Estimates of occurrence times of seldom events in regenerative processes, Engineering Cybernetics, v.23, N 2, 214–216.Google Scholar
  11. Soloviev, A.D. (1983). Analytical methods of reliability computation and estimations. In B.V. Gnedenko (Ed.) “Problems of mathematical reliability theory” (in Russian), Radio i Sviaz, Moscow.Google Scholar
  12. Zolotarev, V.M. (1976). Metric distances in spaces of random variables and their distributions, Math.USSR Sbornik, v.30, N 3.Google Scholar
  13. Zolotarev, V.M. (1977). General problems of the stability of math. models. Proc. 41-st session Intern.Stat.Institute, New Delhi, XLVII (2), 382-401.Google Scholar
  14. Zolotarev, V.M. (1983). Probability metrics. Theory Prob.Appl., v.XXVIII, N 2.Google Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • V. V. Kalashnikov
    • 1
  1. 1.Institute for Systems StudiesMoscowRussia

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