Semimartingale Stochastic Approximation Procedures and Recursive Estimation

The semimartingale stochastic approximation procedure, namely, the Robbins-Monro type SDE is introduced which naturally includes both generalized stochastic approximation algorithms with martingale noises and recursive parameter estimation procedures for statistical models associated with semimartingales. General results concerning the asymptotic behaviour of the solution are presented. In particular, the conditions ensuring the convergence, rate of convergence and asymptotic expansion are established. The results concerning the Polyak weighted averaging procedure are also presented.