Continuous-time stochastic approximation: Convergence and asymptotic efficiency. (English) Zbl 0851.60028
Summary: A continuous-time stochastic approximation algorithm is proposed. It is shown that the estimate \(x_t\) is strongly consistent and the averaged estimate \(\overline x_t = (1/t) \int^t_0 x_s ds\) is asymptotically efficient. The characteristics of the results 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 \(x_t\); 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.
Keywords:
continuous-time stochastic approximation; efficiency; slow gain; averaging; random truncationsReferences:
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