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Strong representation of an adaptive stochastic approximation procedure

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  • Schwabe, R.

Abstract

We consider a rather general one-dimensional stochastic approximation algorithm where the steplengths might be random. Without assuming a martingale property of the random noise we obtain a strong representation by weighted averages of the error terms. We are able to apply the representation to an adaptive process in the case where the random noise is a martingale difference sequence as well as in the case where the random noise is weakly dependent and some moment conditions are statisfied.

Suggested Citation

  • Schwabe, R., 1986. "Strong representation of an adaptive stochastic approximation procedure," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 115-130, October.
    • Handle: RePEc:eee:spapps:v:23:y:1986:i:1:p:115-130
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    Cited by:

    1. Rydén, Tobias, 1997. "On recursive estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 79-96, February.

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