article · Monte Carlo Methods and Applications
This research investigates the use of Importance Sampling to enhance the estimation of rare events within Hidden Markov Models. The method aims to determine steady-state quantities more rapidly and accurately than standard Monte Carlo simulations. It offers a notable reduction in the time required for simulations. The effectiveness and practical utility of this approach were demonstrated through a basic numerical example.
Accurately and efficiently modelling rare events is crucial in many fields, such as risk assessment or system reliability. This method provides a faster and more precise way to estimate these infrequent but potentially high-impact occurrences within complex systems, improving predictive capabilities and decision-making.
This early-stage research offers a methodological improvement for modelling rare events in Hidden Markov Models. It could be applied by risk analysts, financial modellers, or engineers to develop more efficient and accurate simulation tools for systems where rare but critical events occur. The abstract indicates a basic numerical example, suggesting further development is needed for real-world application.
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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.
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DOI: 10.1515/mcma-2026-3014
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