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The semimartingale stochastic approximation procedure, na- mely, the Robbins-Monro type SDE is introduced which naturally includes both generalized stochastic approximation algorithms with martingale no- ises and recursive parameter estimation procedures for statistical models associated with semimartingales. General results concerning the asymp- totic 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 pro- cedure are also presented.

Semimartingale stochastic approximation procedure and recursive estimation