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 L₁ consistency and L₂ asymptotic normality are established. The L₂ asymptotic normality implies √n convergence rates for L₂ deviation.