Convergence of Stochastic approximation algorithm under irregular conditions

We consider a class of stochastic approximation (SA) algorithms for

solving a system of estimating equations. The standard condition for

the convergence of the SA algorithms is that the estimating functions

are locally Lipschitz continuous. Here, we show that this condition can

be relaxed to the extent that the estimating functions are bounded

and continuous almost everywhere. As a consequence, the use of the

SA algorithm can be extended to some problems with irregular estimating

functions. Our theoretical results are illustrated by solving an

estimation problem for exponential power mixture models.