The present paper focuses on the problem of sampling from a given target distribution $\pi$ 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 $\pi$ 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.

翻译：本文聚焦于在一般状态空间上从给定目标分布$\pi$进行采样的问题。为此，我们引入了一类新型不可逆马尔可夫链，每条链定义在扩展的状态空间上，并具有一个以$\pi$为边际分布的遍历概率测度。所提出的方法受Kac定理的新形式启发，能够平滑地结合全局动力学与局部动力学。在温和条件下，相应的马尔可夫转移核可证明是不可约的且具有哈里斯递归性。此外，我们证明在全局与局部动力学的适当条件下，几何遍历性成立。最后，我们通过数值实验展示了所提方法的应用及其相对于现有马尔可夫链蒙特卡洛（MCMC）算法的潜在优势。