On Fixed Gain Recursive Estimation Processes

An important class of xed gain recursive estimation processes can be approximated by random diierential equations, the right hand sides of which are L-mixing random elds. It will be shown that the solution trajectories of these random diierential equations follow the trajectories of the corresponding deterministic diierential equation obtained by averaging so that the tracking error is majorated by an L-mixing process,the moments of which can be estimated. The result is applied to prove a theorem on the pathwise tracking ability of a time-varying recursive estimation scheme.