This thesis is concerned with the Bayes sequential estimation of parameters of a two state Markov process by continuous observation.
The process is observed until a pair of changes of state occurs at which time a decision will be made whether to stop the sampling or to continue the observation until the next pairs of changes of state.
The loss is assumed to be of the form $(\Theta-d)^e\Theta^{-P}$ and two types of cost are considered; cost proportional to the number of sampling periods and cost proportional to sampling time.
Optimal stopping regions and sufficient conditions for optimality are obtained explicitly for both r known and unknown cases, where r is the ratio of the two parameters.
For the case of large parameters where state transitions occur so frequently that it is difficult to make decisions at every pair of state transitions, the problem of sequential estimation by grouped observations is also considered.
