Stochastic Approximation: Convergence Results for Dependent Observations.
COLORADO STATE UNIV FORT COLLINS DEPT OF ELECTRICAL ENGINEERING
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Robbins-Monro stochastic approximation algorithms arise in many single- and multi-sensor signal processing applications where there is a need to adapt to unknown statistical parameters. In this report a theorem is stated and proved that ensures almost sure a.s. convergence of the Robbins-Monro algorithm provided the observation sequence satisfies certain covariance ergodicity conditions. These conditions are related to the conditions required to obtain a.s. convergence of the usual covariance estimator. Author