Sequential Estimation in an Exponential Class of Markov Processes

Abstract

Sequential estimation problems have been considered for some special classes of Markov processes in the last ten years. In this note, a general exponential class of Markov processes is studied. Many widely used models for stochastic processes are of this type. The exponential class under consideration is closely related to homogeneous processes with independent increments by random time transformations. In the sequential case, i. e. given a Markov stopping time, an inequality of Cramér-Rao-Wolfowitz type is stated and properties of efficient sequential estimation procedures are derived. As an application, more detailed results are given for a special branching process. In particular, the distribution of the estimate can be obtained and the problem of constructing minimum variance unbiased estimates is considered.