Strong approximations and sequential change-point analysis for diffusion processes

In this paper ergodic diffusion processes depending on a parameter in the drift are considered under the assumption that the processes can be observed continuously. Strong approximations by Wiener processes for a stochastic integral and for the estimator process constructed by the one-step procedure of Le Cam are obtained. Applying these approximations, a CUSUM-type procedure is developed for the sequential testing of changes in the parameter.