Theoretical properties of quasi-stationary Monte Carlo methods

This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems.We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target density of interest.We also quantify the rate of convergence to quasi-stationarity by relating the killed diffusion to an appropriate Langevin diffusion.As an example, we consider in detail a killed Ornstein.Uhlenbeck process with Gaussian quasi-stationary distribution.