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arXiv · 1707.08036

Theoretical properties of quasi-stationary Monte Carlo methods

Andi Q. Wang·Martin Kolb·Gareth O. Roberts·David Steinsaltz
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Abstract

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.

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Andi Q. Wang, Martin Kolb, Gareth O. Roberts, David Steinsaltz. 2018-12-06. Theoretical properties of quasi-stationary Monte Carlo methods. https://doi.org/10.1214/18-aap1422

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