On Stochastic Approximation for Random Processes with Continuous Time

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Previous article Next article On Stochastic Approximation for Random Processes with Continuous TimeT. P. KrasulinaT. P. Krasulinahttps://doi.org/10.1137/1116073PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Herbert Robbins and , Sutton Monro, A stochastic approximation method, Ann. Math. Statistics, 22 (1951), 400–407 MR0042668 0054.05901 CrossrefGoogle Scholar[2] J. Kiefer and , J. Wolfowitz, Stochastic estimation of the maximum of a regression function, Ann. Math. Statistics, 23 (1952), 462–466 MR0050243 0049.36601 CrossrefGoogle Scholar[3] Miloslav Driml and , J. Nedoma, Stochastic approximations for continuous random processes, Trans. 2nd Prague Conf. Information Theory, Publ. House Czechoslovak Acad. Sci., Prague, Academic Press, New York, 1960, 145–158 MR0126877 0098.32202 Google Scholar[4] Jerome Sacks, Asymptotic distribution of stochastic approximation procedures, Ann. Math. Statist., 29 (1958), 373–405 MR0098427 0229.62010 CrossrefGoogle Scholar[5] David J. Sakrison, A continuous Kiefer-Wolfowitz procedure for random processes, Ann. Math. Statist., 35 (1964), 590–599 MR0161445 0131.35905 CrossrefGoogle Scholar[6] V. A. Volkonskii˘ and , Yu. A. Rozanov, Some limit theorems for random functions. I, Theor. Probability Appl., 4 (1959), 178–197 MR0121856 0092.33502 LinkGoogle Scholar[7] I. A. Ibragimov, Some limit theorems for stationary processes, Theory Prob. Applications, 7 (1962), 349–382 10.1137/1107036 0119.14204 LinkGoogle Scholar[8] S. G. Mikhlin, Lectures on Linear Integral Equations, Fizmatgiz, Moscow, 1959, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Gradient procedures for stochastic approximation with dependent noise and their asymptotic behaviourInternational Journal of Systems Science, Vol. 16, No. 8 | 10 May 2007 Cross Ref Some Limit Theorems for Processes with Random TimeA. N. BorodinTheory of Probability & Its Applications, Vol. 24, No. 4 | 17 July 2006AbstractPDF (1390 KB)Sufficient conditions for convergence of stochastic approximation algorithms for random processes with continuous timeCybernetics, Vol. 15, No. 6 | 1 Nov 1979 Cross Ref A Stochastic Approximation Procedure in the Case of Weakly Dependent ObservationsA. N. BorodinTheory of Probability & Its Applications, Vol. 24, No. 1 | 17 July 2006AbstractPDF (1321 KB)Recursive stochastic gradient procedures in the presence of dependent noiseStochastic Optimization Cross Ref Volume 16, Issue 4| 1971Theory of Probability & Its Applications575-746 History Submitted:07 July 1969Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1116073Article page range:pp. 674-682ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics