Abstract
We consider a sequence (Z n ) n≥1 defined by a general multivariate stochastic approximation algorithm and assume that (Z n ) converges to a solution z* almost surely. We establish the compact law of the iterated logarithm for Z n by proving that, with probability one, the limit set of the sequence (Z n − z*) suitably normalized is an ellipsoid. We also give the law of the iterated logarithm for the l p norms, p ∈ [1, ∞], of (Z n − z*).
ACKNOWLEDGMENT
We thank the anonymous referee for his constructive comments.