论文标题
无限尺寸分段确定性马尔可夫流程
Infinite Dimensional Piecewise Deterministic Markov Processes
论文作者
论文摘要
在本文中，我们旨在构建良好的分段确定性蒙特卡洛方法的无限尺寸版本，例如有弹性粒子采样器，Zig-Zag Sampler和Boomerang Sampler。为此，我们为具有无限事件强度的分段确定性Markov过程（PDMP）提供了一个抽象的无限维度框架。我们使用低调技术进一步发展了指数融合到无限尺寸飞旋镖采样器的平衡。此外，我们确定无限尺寸的飞旋镖采样器如何接受有限的尺寸近似，使其适合计算机模拟。
In this paper we aim to construct infinite dimensional versions of well established Piecewise Deterministic Monte Carlo methods, such as the Bouncy Particle Sampler, the Zig-Zag Sampler and the Boomerang Sampler. In order to do so we provide an abstract infinite-dimensional framework for Piecewise Deterministic Markov Processes (PDMPs) with unbounded event intensities. We further develop exponential convergence to equilibrium of the infinite dimensional Boomerang Sampler, using hypocoercivity techniques. Furthermore we establish how the infinite dimensional Boomerang Sampler admits a finite dimensional approximation, rendering it suitable for computer simulation.
