Generalized Look‐Ahead Methods for Computing Stationary Densities

The look‐ahead estimator is used to compute densities associated with Markov processes via simulation. We study a framework that extends the look‐ahead estimator to a broader range of applications. We provide a general asymptotic theory for the estimator, where both L 1 consistency and L 2 asymptotic normality are established. The L 2 asymptotic normality implies √n convergence rates for L 2 deviation.