# An approximation scheme for quasi-stationary distributions of killed diffusions

arXiv: https://arxiv.org/abs/1808.07086 · HTML: https://mlsanity.com/paper/1808.07086/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Aug 2018.

## Built on by (most cited first, 1 of 1)

- [Learn Quasi-stationary Distributions of Finite State Markov Chain](https://mlsanity.com/paper/2111.11213/) (2021)

## Abstract (arXiv)

In this paper we study the asymptotic behavior of the normalized weighted empirical occupation measures of a diffusion process on a compact manifold which is killed at a smooth rate and then regenerated at a random location, distributed according to the weighted empirical occupation measure. We show that the weighted occupation measures almost surely comprise an asymptotic pseudo-trajectory for a certain deterministic measure-valued semiflow, after suitably rescaling the time, and that with probability one they converge to the quasi-stationary distribution of the killed diffusion. These results provide theoretical justification for a scalable quasi-stationary Monte Carlo method for sampling from Bayesian posterior distributions.