A General Importance Sampling Framework Based on Markov Random Walks

For stochastic models driven by hidden Markov processes, this paper proposes a general importance sampling framework that separately distorts observable and hidden processes, achieving logarithmic-efficient estimation through a link function that directly minimizes estimator variance. This framework can be used to estimate overflow probabilities under epidemic models and the systemic risk co-dependence measure CoVaR, overcoming the nonlinearity limitations of traditional importance sampling methods.