Interval Evaluation of Stationary State Probabilities for Markov Set-Chain Models

Abstract

Interval estimation problem for stationary state probability distribution of set-chain Markov model uncertainties of transition matrix parameters is considered. To obtain final probability vector interval estimates, an optimization approach is proposed using regularized Lagrange function. To solve the obtained regularized bilinear programming problem, computational gradient algorithms are used with ensures the stability of resulting estimates. An example of Markov model of a Bonus-Malus system with interval uncertainties of claim flow intensity is presented.