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
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.
stochastic approximation, martingale methods, stochastic exponents, stochastic Lyapunov method.
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Theory of Probability and its Applications, 2000, 44:2, 333–360
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
\by E.~Valkeila, A.~V.~Melnikov
\paper Martingale models of stochastic approximation and their convergence
\jour Teor. Veroyatnost. i Primenen.
\jour Theory Probab. Appl.
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