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Semimartingale stochastic approximation procedure and recursive estimation

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Abstract

The semimartingale stochastic approximation procedure, precisely, the Robbins-Monro type SDE, is introduced, which naturally includes both generalized stochastic approximation algorithms with martingale noises and recursive parameter estimation procedures for statistical models associated with semimartingales. General results concerning the asymptotic behavior of the solution are presented. In particular, the conditions ensuring the convergence, the rate of convergence, and the asymptotic expansion are established. The results concerning the Polyak weighted averaging procedure are also presented.

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Authors and Affiliations

  1. Georgian-American University, Business School, Tbilisi, Georgia

    N. Lazrieva & T. Toronjadze

  2. A. Razmadze Mathematical Institute, Tbilisi, Georgia

    N. Lazrieva

  3. Department of Mathematics, Royal Holloway, University of London, Egham, Surrey, UK

    T. Sharia

Authors
  1. N. Lazrieva
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  2. T. Sharia
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  3. T. Toronjadze
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Correspondence to T. Sharia.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 45, Martingale Theory and Its Application, 2007.

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Lazrieva, N., Sharia, T. & Toronjadze, T. Semimartingale stochastic approximation procedure and recursive estimation. J Math Sci 153, 211–261 (2008). https://doi.org/10.1007/s10958-008-9127-y

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