Asymptotic law in sequential estimation of a change point (Q1210129)

For the change point problem with known distributions, the first hitting times of a recursively defined stochastic process are suggested as sequential estimators of the change point. The Page-Hinckley detector is a special case. Extending known convergence theorems on recursive processes of the considered kind, the (Gaussian) limits of the suitably rescaled process and of its hitting times are derived.