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A law of the iterated logarithm for stochastic approximation procedures in d-dimensional Euclidean space


  • Koval, Valery
  • Schwabe, Rainer


In this paper, we investigate the rate of convergence for general d-dimensional stochastic approximation procedures and present an explicit expression for the asymptotic bounds in the law of the iterated logarithm.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:spapps:v:105:y:2003:i:2:p:299-313

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    References listed on IDEAS

    1. Einmahl, Uwe, 1989. "Extensions of results of Komlós, Major, and Tusnády to the multivariate case," Journal of Multivariate Analysis, Elsevier, vol. 28(1), pages 20-68, January.
    2. 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.
    3. 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.
    4. 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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