Estimation and decision for observations derived from martingales: Part II

The development of an approach for obtaining statistical inferences about nonobservable processes that influence a process which can be observed directly and which is assumed to be a mixture of continuous and discontinuous components is continued. The approach is based on probability-measure transformations and consists of finding the conditional probability of a nonobservable event in terms of the prior probability of that event and a functional of the observations . The topics studied include optimal filtering, smoothing, and prediction estimates of the nonobservable process; -ary hypothesis testing; performance lower-bounds; and stochastic control.