Abstract
The rate of convergence of a linear stochastic approximation procedure inR d is studied under fairly general assumptions on the coefficients of the equation.
Similar content being viewed by others
References
A. P. Korostelev,Stochastic Recursion Procedures (Local Properties) [in Russian], Nauka, Moscow (1984).
H. Walk, “Limit behavior of stochastic approximation processes,”Statist, and Decis.,6, No. 1–2, 109–128 (1988).
L. Ljung,Convergence of Recursive Stochastic Algorithms, Report 7403, Department of Automatic Control, Lund Institute of Technology (1974).
H. Walk and L. Zsido, “Convergence of the Robbins-Monro method for linear problems in a Banach space,”J. Math. Anal. Appl.,139, No. 1, 152–177 (1989).
V. V. Voevodin and Yu. A. Kuznetsov,Matrices and Calculations [in Russian], Nauka, Moscow (1984).
V. A. Koval', “Comparison principles for multidimensional Gaussian Markovian sequences and Gaussianm-Markovian sequences,” in:Stochastic Systems and Applications [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1990), pp. 60–65.
V. A. Koval', “Convergence of Gaussian sequences to zero and the asymptotic behavior of solutions of stochastic recursion equations,” in:Stochastic Analysis and Applications [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1989), pp. 64–70.
V. A. Egorov, “On the law of iterated logarithm”,Teor. Ver. Primen.,14, No. 4, 722–729 (1969).
V. V. Buldygin and V. A. Koval',Asymptotic Behavior of Solutions of Stochastic Difference Equations [in Russian], Preprint No. 91.24, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1991).
V. A. Koval',Asymptotic Behavior of Solutions of Stochastic Recursion Equations [in Russian], Author's Abstract of the Candidate Degree Thesis (Physics and Mathematics), Kiev (1991).
V. V. Buldygin and A. B. Kharazishvili,Brunn-Minkowski Inequality and Applications [in Russian], Naukova Dumka, Kiev (1985).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 8, pp. 997–1002, August, 1994.
Rights and permissions
About this article
Cite this article
Koval', V.A. On the rate of convergence of stochastic approximation procedures. Ukr Math J 46, 1093–1100 (1994). https://doi.org/10.1007/BF01056170
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01056170