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On the almost sure asymptotic behaviour of stochastic algorithms

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  • Pelletier, Mariane

Abstract

We study the almost sure asymptotic behaviour of decreasing stepsized stochastic algorithms used for the search of zeros of a function. We prove a law of the iterated logarithm, which gives the almost sure convergence rate of the algorithm, and we establish a quadratic strong law of large numbers.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:78:y:1998:i:2:p:217-244
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    References listed on IDEAS

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    1. Alain Breton & Alexander Novikov, 1995. "Some results about averaging in stochastic approximation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 153-171, December.
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    Cited by:

    1. 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.
    2. Yves F. Atchadé, 2006. "An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 235-254, June.
    3. Claire Boyer & Antoine Godichon-Baggioni, 2023. "On the asymptotic rate of convergence of Stochastic Newton algorithms and their Weighted Averaged versions," Computational Optimization and Applications, Springer, vol. 84(3), pages 921-972, April.
    4. Costa, Manon & Gadat, Sébastien & Bercu, Bernard, 2020. "Stochastic approximation algorithms for superquantiles estimation," TSE Working Papers 20-1142, Toulouse School of Economics (TSE).
    5. Koval, Valery & Schwabe, Rainer, 2003. "A law of the iterated logarithm for stochastic approximation procedures in d-dimensional Euclidean space," Stochastic Processes and their Applications, Elsevier, vol. 105(2), pages 299-313, June.

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    1. S. Pergamenshchikov, 1998. "Asymptotic Expansions for the Stochastic Approximation Averaging Procedure in Continuous Time," Statistical Inference for Stochastic Processes, Springer, vol. 1(2), pages 197-223, May.

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