Continuous-time stochastic approximation: Convergence and asymptotic efficiency
Chen Han-Fu · Stochastics and stochastics reports · 1994
A continuous-time stochastic approximation algorithm is proposed. It is shown that the estimate xt is strongly consistent and the averaged estimate is asymptotically efficient. The characteristics of the results obtained in the paper are as follows: 1) No growth rate restriction is imposed on the regression function; 2) No boundedness assumption is a priori made on the estimate xt ; 3) The method for proving strong consistency differs from the martingale approach and is an improvement of the ODE method; 4) Slow gains, randomly varying truncation and averaging technique are used for estimation