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Teor. Veroyatnost. i Primenen., 1999, Volume 44, Issue 2, Pages 278–311 (Mi tvp764)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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.

DOI: https://doi.org/10.4213/tvp764

Full text: PDF file (1474 kB)

English version:
Theory of Probability and its Applications, 2000, 44:2, 333–360

Bibliographic databases:

Received: 17.07.1997
Revised: 11.11.1998

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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\paper Martingale models of stochastic approximation and their convergence
\jour Teor. Veroyatnost. i Primenen.
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\zmath{https://zbmath.org/?q=an:0974.62063}
\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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Lazrieva N., Toronjadze T., “Recursive Estimation Procedures For One-Dimensional Parameter of Statistical Models Associated With Semimartingales”, Trans. A Razmadze Math. Inst., 171:1 (2017), 57–75  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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