Bulletin of the Australian Mathematical Society

Research Article

On the almost sure convergence of a general stochastic approximation procedure

S. N. Evansa1 and N. C. Webera2

a1 Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge, England.

a2 Department of Mathematical Statistics, University of Sydney, New South Wales 2006, Australia.


A set of conditions for the almost sure convergence of a stochastic iterative procedure is given. The conditions are framed in terms of the behaviour of the random adjustment made the n-th step rather than in terms of some underlying regression model.

(Received December 20 1985)