An approximation scheme for quasi-stationary distributions of killed diffusions
An approximation scheme for quasi-stationary distributions of killed diffusions
复制标题
DOI：
10.1016/j.spa.2019.09.010
复制
发表时间：
2018-08
影响因子：
1.4
通讯作者：
Andi Q. Wang;G. Roberts;D. Steinsaltz
中科院分区：
文献类型：
--
作者：
Andi Q. Wang;G. Roberts;D. Steinsaltz
本文研究了紧致流形上扩散过程的归一化加权经验占位测度的渐近性态，该扩散过程以光滑速率被杀死，然后在随机位置再生，按加权经验占位测度分布.我们表明，加权占领措施几乎肯定包括一个渐进的伪轨迹，一定的确定性测量值的半流，经过适当的重新调整的时间，并与概率1，他们收敛到准稳态分布的死亡扩散。这些结果提供了一个可扩展的准平稳蒙特卡罗方法从贝叶斯后验分布抽样的理论依据。
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.