On the Convergence to Diffusion Processes
Alexandr Alekseevich Borovkov · Theory of Probability and Its Applications · 1967
Previous article Next article On the Convergence to Diffusion ProcessesA. A. BorovkovA. A. Borovkovhttps://doi.org/10.1137/1112052PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. A. Borovkov, On the convergence of weakly-dependent processes to Wiener-type, Theory Prob. Applications, 12 (1967), 159–186 10.1137/1112024 0214.16202 LinkGoogle Scholar[2] I. I. Gikhman and , A. V. Skorokhod, Introduction to the Theory of Random Processes, Izd-vo “Nauka”, Moscow, 1965, (In Russian.) Google Scholar[3] A. M. Il'in, , A. S. Kalašnikov and , O. A. Olei˘nik, Second-order linear equations of parabolic type, Uspehi Mat. Nauk, 17 (1962), 3–146, (In Russian.) MR0138888 Google Scholar[4] A. Ya. Khinchin, Asymptotic Laws of Probability Theory, ONTI, Moscow—Leningrad, 1936, (In Russian.) Google Scholar[5] A. V. Skorokhod, Stochastic equations for diffusion processes in a bounded region, Theory Prob. Applications, 6 (1961), 264–274 10.1137/1106035 LinkGoogle Scholar[6] M. I. Frei˘dlin, Application of K. Itô's stochastic equations to the investigation of the second boundary problem, Proc. Sixth All-Union Conf. Theory Prob. and Math. Statist. (Vilnius, 1960) (Russian), Gosudarstv. Izdat. Političesk. i Naučn. Lit. Litovsk. SSR, Vilnius, 1962, 173–176, (In Russian.) MR0200608 Google Scholar[7] J. L. Doob, Martingales and one-dimensional diffusion, Trans. Amer. Math. Soc., 78 (1955), 168–208 MR0070885 0068.11301 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Analysis, Design, and Control of Queueing SystemsOperations Research, Vol. 50, No. 1 | 1 Feb 2002 Cross Ref Weak convergence in applied probabilityStochastic Processes and their Applications, Vol. 2, No. 3 | 1 Jul 1974 Cross Ref Heavy Traffic Limit Theorems for Queues: A SurveyMathematical Methods in Queueing Theory | 1 Jan 1974 Cross Ref On the transition from a Markov chain to a continuous time processStochastic Processes and their Applications, Vol. 1, No. 4 | 1 Oct 1973 Cross Ref On Convergence of Semi-Markov Multiplication Processes with Drift to a Diffusion ProcessTheory of Probability & Its Applications, Vol. 17, No. 3 | 17 July 2006AbstractPDF (410 KB)Convergence to Markov processesUkrainian Mathematical Journal, Vol. 21, No. 3 | 1 Jan 1970 Cross Ref On limit laws for service processes in multi-channel systemsSiberian Mathematical Journal, Vol. 8, No. 5 | 1 September 1967 Cross Ref Volume 12, Issue 3| 1967Theory of Probability & Its Applications History Submitted:17 January 1966Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1112052Article page range:pp. 405-431ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics