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An Almost Sure Central Limit Theorem for Stochastic Approximation Algorithms

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  • Pelletier, Mariane

Abstract

We prove an almost sure central limit theorem for some multidimensional stochastic algorithms used for the search of zeros of a function and known to satisfy a central limit theorem. The almost sure version of the central limit theorem requires either a logarithmic empirical mean (in the same way as in the case of independent identically distributed variables) or another scale, depending on the choice of the algorithm gains.

Suggested Citation

  • Pelletier, Mariane, 1999. "An Almost Sure Central Limit Theorem for Stochastic Approximation Algorithms," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 76-93, October.
    • Handle: RePEc:eee:jmvana:v:71:y:1999:i:1:p:76-93
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    References listed on IDEAS

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    1. Lacey, Michael T. & Philipp, Walter, 1990. "A note on the almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 201-205, March.
    2. Pelletier, Mariane, 1998. "On the almost sure asymptotic behaviour of stochastic algorithms," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 217-244, November.
    3. Zhu, Yunmin, 1996. "Asymptotic Normality for a Vector Stochastic Difference Equation with Applications in Stochastic Approximation," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 101-118, April.
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