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Teor. Veroyatnost. i Primenen., 1983, Volume 28, Issue 4, Pages 769–775 (Mi tvp2226)  

Short Communications

A note on upper functions for stochastic approximation

A. P. Korostelev

Moscow

Abstract: For the Robbins–Monro process (1) we study the upper functions $g(t)$ such that $\displaystyle \limsup_{t\to\infty}(X(t)-\theta)/g(t)=1$ a. s. In the case of continuous time $\xi(t)$ in (1) is the process with homogeneous independent increments; in the case of discrete time $d\xi(s)$, are i. i. d. random variables. The one-dimensional procedure (2) is considered in theorem 1, the multidimensional procedure (11) is studied in theorem 2. All results are obtained under the assumption of finiteness of moment generating function and are based on the theorems on large deviations for Markov processes [10].

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English version:
Theory of Probability and its Applications, 1984, 28:4, 806–811

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Received: 12.06.1980

Citation: A. P. Korostelev, “A note on upper functions for stochastic approximation”, Teor. Veroyatnost. i Primenen., 28:4 (1983), 769–775; Theory Probab. Appl., 28:4 (1984), 806–811

Citation in format AMSBIB
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\by A.~P.~Korostelev
\paper A note on upper functions for stochastic approximation
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 4
\pages 769--775
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=726903}
\zmath{https://zbmath.org/?q=an:0558.62074|0536.62064}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 4
\pages 806--811
\crossref{https://doi.org/10.1137/1128079}
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