RECURSIVE-IDENTIFICATION IN CONTINUOUS-TIME STOCHASTIC-PROCESSES

Recursive parameter estimation in diffusion processes is considered. F irst, stability and asymptotic properties of the global, off-line MLE (maximum likelihood estimator) are obtained under explicit conditions. The MLE evolution equation is then derived by employing a generalized Ito differentiation rule. This equation, which is highly sensitive to initial conditions, is then modified to yield an algorithm (infinite dimensional in general) which results in an estimator that, irrespecti ve of initial conditions, is consistent and asymptotically efficient a nd in addition, converges rapidly to the MLE. The structure of the alg orithm indicates that well known gradient and Newton type algorithms a re first-order approximations. The results cover a wide class of proce sses, including nonstationary or even divergent ones.