Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which implies quantitative bounds on the total variation between the marginal distributions of the two processes. Finally two results are established regarding the invariant measures of PDMPs. A practical condition to show that a probability measure is invariant for the associated PDMP semi-group is presented. In a second time, a bound on the invariant probability measures in $V$-norm of two PDMPs following the same differential flow is established. This last result is then applied to study the asymptotic bias of some non-exact PDMP MCMC methods.
翻译：在一个总的框架内研究小的确定性 Markov 进程(PDMPs) 。 首先, 不同的构造被证明是等效的。 其次, 我们引入了两个PDMPs在相同差异流之后的组合, 这意味着两个进程边际分布之间总差异的量化界限。 最后, 确定了两个关于PDMPs的不变化性测量结果。 一个实际条件是显示对相关的 PDMP 半组进行概率测量是无变量的。 第二次, 我们设定了两个PDMPs在相同差异流之后的不变概率值以$- 诺姆为基值的组合。 最后一个结果被用于研究某些非典型的 PDMP MC 方法的无规律性偏差。
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