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 also killed at a given rate and 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 quasistationary distribution of the killed diffusion. These results provide theoretical justification for a scalable quasistationary Monte Carlo method for sampling from Bayesian posterior distributions in large data settings.

中文翻译：

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抑制扩散的准平稳分布的近似方案

在本文中，我们研究了紧凑流形上扩散过程的归一化加权经验占用度量的渐近行为，该流形也以给定速率被杀死并在随机位置再生，根据加权经验占用度量分布。我们表明，在适当地重新调整时间后，加权占用测量几乎肯定包含某个确定性测量值半流的渐近伪轨迹，并且它们以概率收敛到抑制扩散的准平稳分布。这些结果为在大数据设置中从贝叶斯后验分布中采样的可扩展准平稳蒙特卡罗方法提供了理论依据。