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Teoriya Veroyatnostei i ee Primeneniya, 1999, Volume 44, Issue 2, Pages 278–311
DOI: https://doi.org/10.4213/tvp764 (Mi tvp764) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Martingale models of stochastic approximation and their convergence

E. Valkeilaa, A. V. Melnikovb

a Department of Mathematics, University of Helsinki, Finland
b Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (1474 kB) Citations (4)
DOI: https://doi.org/10.4213/tvp764
Abstract: Procedures of stochastic approximation are studied from a general theory of stochastic processes point of view. The results on convergence are obtained by the uniform methods both in the case of discrete and of continuous time. The asymptotic analysis (a.s. convergence, asymptotic normality) of procedures is based on the Lyapunov stochastic method, and a study of the rate of convergence of algorithms of stochastic approximation is based on the law of iterated logarithm for martingales.
Keywords: stochastic approximation, martingale methods, stochastic exponents, stochastic Lyapunov method.
Received: 17.07.1997
Revised: 11.11.1998
English version:
Theory of Probability and its Applications, 2000, Volume 44, Issue 2, Pages 333–360
DOI: https://doi.org/10.1137/S0040585X97977549
Bibliographic databases:
Language: Russian
Citation: E. Valkeila, A. V. Melnikov, “Martingale models of stochastic approximation and their convergence”, Teor. Veroyatnost. i Primenen., 44:2 (1999), 278–311; Theory Probab. Appl., 44:2 (2000), 333–360
Citation in format AMSBIB
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\by E.~Valkeila, A.~V.~Melnikov
\paper Martingale models of stochastic approximation and their convergence
\jour Teor. Veroyatnost. i Primenen.
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\pages 278--311
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\transl
\jour Theory Probab. Appl.
\yr 2000
\vol 44
\issue 2
\pages 333--360
\crossref{https://doi.org/10.1137/S0040585X97977549}
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  • https://www.mathnet.ru/eng/tvp764
  • https://doi.org/10.4213/tvp764
  • https://www.mathnet.ru/eng/tvp/v44/i2/p278
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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