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Theoretical properties of quasi-stationary Monte Carlo methods. (English) Zbl 1408.60072
Summary: 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.

MSC:
60J60 Diffusion processes
65C05 Monte Carlo methods
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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