Minimax sequential procedures for Markov-additive processes

The paper deals with the problem of finding optimal, under minimax criterion, sequential estimation procedures for Markov-additive processes. The loss in estimating is assumed to consist of the error of estimation as well as the cost of observing the process (for example, the cost depending on arrivals at a queueing system up to the moment of stopping). The idea and tools are exhibited to obtain minimax sequential procedures for estimating important quantities of unknown parameters of Markov-additive processes. Using a weighted squared error loss and assuming the cost is a function of the additive component of a Markov-additive process, a class of minimax sequential procedures is derived explicitly for estimating the ratios between transition intensities of the embedded Markov chain and the mean value parameter of the additive part of the process considered.