Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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.
Anichkin, S.A. and V.V. Kalashnikov (1981). Continuity of random sequences and approximation of Markov chains. Adv.Appl.Prob., 13, 402–414.
Kalashnikov, V.V. (1978a). Qualitative analysis of the behaviour of complex systems by trial functions (in Russian), Nauka, Moscow.
Kalashnikov, V.V. (1978b). Solution of the approximation problem for a denumerable Markov chain. Engineering Cybernetics, v.16, N 3.
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.
Kalashnikov, V.V. (1981b). Methods of continuity estimates for states enlarging problem. Stability problems for stochastic models, 48–53, (in Russian) VNIISI, Moscow.
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.
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.
Kalashnikov, V.V. (1983c). An estimate of convergence rate in Renyi’s theorem. Stability problems for stochastic models, 48–57 (in Russian), VNIISI, Moscow.
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.
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.
Zolotarev, V.M. (1976). Metric distances in spaces of random variables and their distributions, Math.USSR Sbornik, v.30, N 3.
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.
Zolotarev, V.M. (1983). Probability metrics. Theory Prob.Appl., v.XXVIII, N 2.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kalashnikov, V.V. (1986). Approximation of some stochastic models. In: Janssen, J. (eds) Semi-Markov Models. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0574-1_17
Download citation
DOI: https://doi.org/10.1007/978-1-4899-0574-1_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-0576-5
Online ISBN: 978-1-4899-0574-1
eBook Packages: Springer Book Archive