Construction of Confidence Sets for Markov Chain Model

The problem of forecasting the state probabilities vector for a stationary Markov chain with discrete time in case of transition probabilities are not exactly known and measured during the system operation is investigated. An auxiliary dynamic system with uncertainty and observation showing the dynamics of the state probabilities vector is constructed. Two approaches to the determination of the guaranteed with a given probability estimates are proposed. The first approach uses confidence sets for rows of the matrix of transition probabilities and the ellipsoidal calculus. The second approach is based on simulation and finding a sample quantile of an objective function, which determines the form of a confidence set for the system state.