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.
"Theoretical properties of quasi-stationary Monte Carlo methods." Ann. Appl. Probab. 29 (1) 434 - 457, February 2019. https://doi.org/10.1214/18-AAP1422