Martingale models of stochastic approximation and their convergence (Q2711124)

Stochastic calculus is used to provide advanced results in stochastic approximation problems. The involved procedure leads to the solution of a stochastic differential equation with not necessarily continuous driving semi-martingale. As the time parameter goes to infinity, this solution converges a.s. to the solution of the initial problem. Under additional conditions, the asymptotic normality of the procedure is obtained. A.s. convergence and asymptotic normality are also considered for the averaged procedures. The law of iterated logarithm for locally square integrable martingales is used to obtain sharp estimates. The paper ends with an application of the previous results to discrete time processes.