Steady state Hidden Markov Model with rare events

Abstract Importance sampling is utilized to enhance the Hidden Markov Models’ rare events estimation, yielding results rapidly and accurately than with standard Monte Carlo methods. We study the estimation of the steady state quantities of a Hidden Markov Model with rare events, by using the Importance Sampling technique. When compared to standard Monte Carlo simulations, this method offer a notable reduction in simulation time. The effectiveness and practicality of the approach are illustrated through a basic numerical example.