Convergence in distribution of LMS-type adaptive parameter estimates

We study the asymptotic behavior of parameter estimates generated by LMS (least mean-square)-adaptive estimation algorithms in stationary dependent random situations. We show that, subject to mild, practically reasonable conditions, the estimates converge in distribution. Further, we extend this result to prove a more explicit type of convergence in distribution which explains other observed properties. We then estimate the moments of this limiting distribution and discuss how this relates to the work of others.