利用Kac定理增强您最喜爱的马尔可夫链蒙特卡洛采样器：Kick-Kac传送算法
Boost your favorite Markov Chain Monte Carlo sampler using Kac's theorem: the Kick-Kac teleportation algorithm
AI总结：
本文提出Kick-Kac传送算法，一种基于Kac定理的新型不可逆马尔可夫链，用于从目标分布采样，结合全局与局部动力学，保证不可约、Harris常返及几何遍历性，数值实验显示优于现有MCMC算法。
摘要：
本文关注在一般状态空间上从给定目标分布π中采样的问题。为此，我们引入了一类新的不可逆马尔可夫链，每条链定义在扩展状态空间上，并具有以π为边缘分布的不变概率测度。所提出的方法受Kac定理的新表述启发，允许全局和局部动力学平滑结合。在温和条件下，相应的马尔可夫转移核可证明是不可约且Harris常返的。此外，我们证明在全局和局部动力学的适当条件下，几何遍历性成立。最后，我们数值展示了所提方法的使用及其与现有马尔可夫链蒙特卡洛（MCMC）算法相比的潜在优势。
英文摘要：
The present paper focuses on the problem of sampling from a given target distribution $π$ defined on some general state space. To this end, we introduce a novel class of non-reversible Markov chains, each chain being defined on an extended state space and having an invariant probability measure admitting $π$ as a marginal distribution. The proposed methodology is inspired by a new formulation of Kac's theorem and allows global and local dynamics to be smoothly combined. Under mild conditions, the corresponding Markov transition kernel can be shown to be irreducible and Harris recurrent. In addition, we establish that geometric ergodicity holds under appropriate conditions on the global and local dynamics. Finally, we illustrate numerically the use of the proposed method and its potential benefits in comparison to existing Markov chain Monte Carlo (MCMC) algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
