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February 2019 Theoretical properties of quasi-stationary Monte Carlo methods
Andi Q. Wang, Martin Kolb, Gareth O. Roberts, David Steinsaltz
Ann. Appl. Probab. 29(1): 434-457 (February 2019). DOI: 10.1214/18-AAP1422


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. "Theoretical properties of quasi-stationary Monte Carlo methods." Ann. Appl. Probab. 29 (1) 434 - 457, February 2019.


Received: 1 July 2017; Revised: 1 April 2018; Published: February 2019
First available in Project Euclid: 5 December 2018

zbMATH: 07039129
MathSciNet: MR3910008
Digital Object Identifier: 10.1214/18-AAP1422

Primary: 60J60 , 60J70
Secondary: 47D07 , 65C05

Keywords: $R$-theory , killed diffusions , Quasi-stationary distributions , Quasi-stationary Monte Carlo methods

Rights: Copyright © 2019 Institute of Mathematical Statistics


Vol.29 • No. 1 • February 2019
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