On Sequential Estimation of Parameters of Diffusion Processes

The authors consider the problem of estimating the linear parameters of multivariate stochastic processes described by stochastic differential equations. Sequential designs are constructed that make it possible to estimate the unknown parameters with the requisite accuracy within a finite time. Their asymptotic properties are investigated. A limiting expression that relates the duration of observations and the estimation accuracy is obtained. It is shown that the sequential estimates are asymptotically normal and that they converge with probability 1 and in the mean square.