Abstract
The problem of Bayes sequential estimation of the mean value parameter of continuous time processes with stationary independent increments having exponential-type likelihood functions is considered. Using a weighted square error loss and observing cost involving both a time cost and a state cost, the explicit solutions to the problem are derived. A discrete time approach is taken in which decisions are made at the end of time intervals having lengtht. The examples of optimal procedures in the case when the cost of observation includes a squared state cost are also given.
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