Semimartingale Stochastic Approximation Procedures and Recursive Estimation

Details Semimartingale Stochastic Approximation Procedures and Recursive Estimation Semimartingale Stochastic Approximation Procedures and Recursive Estimation

2007-05-12

arxiv.org/abs/0705.1794v1

Mathematics

Probability

62 pages, no figures

Scientific paper

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.

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