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Teoriya Veroyatnostei i ee Primeneniya, 1999, Volume 44, Issue 3, Pages 661–675
DOI: https://doi.org/10.4213/tvp812 (Mi tvp812) 		 
Short Communications

On stochastic approximation procedures with averaging

A. Le Bretona, A. A. Novikovbc

a LMC/IMAG, Université J. Fourier, France
b Steklov Mathematical Institute, Russian Academy of Sciences
c School of Mathem. Sciences, The University of Technology, Sydney
Full-text PDF (791 kB)
DOI: https://doi.org/10.4213/tvp812
Abstract: Linear multidimensional stochastic approximation procedures in continuous time with martingale errors are considered. An asymptotic behavior of the estimator obtained by trajectory averaging is studied. An asymptotics of integrated squared deviations functionals of the averaged estimator is found. Some results concerning fixed-size confidence regions are presented.
Keywords: stochastic approximation, averaged estimators, martingales.
English version:
Theory of Probability and its Applications, 2000, Volume 44, Issue 3, Pages 591–604
DOI: https://doi.org/10.1137/S0040585X97977823
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. Le Breton, A. A. Novikov, “On stochastic approximation procedures with averaging”, Teor. Veroyatnost. i Primenen., 44:3 (1999), 661–675; Theory Probab. Appl., 44:3 (2000), 591–604
Citation in format AMSBIB
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\by A.~Le Breton, A.~A.~Novikov
\paper On stochastic approximation procedures with averaging
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\pages 661--675
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\zmath{https://zbmath.org/?q=an:1045.62077}
\transl
\jour Theory Probab. Appl.
\yr 2000
\vol 44
\issue 3
\pages 591--604
\crossref{https://doi.org/10.1137/S0040585X97977823}
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  • https://www.mathnet.ru/eng/tvp/v44/i3/p661
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