论文标题
马尔可夫操作员的马尔可夫过程和局部性的路径连续性
Path continuity of Markov processes and locality of Kolmogorov operators
论文作者
论文摘要
我们证明，如果我们获得了Cadlag Markov进程的生成器和在状态空间中的开放域$ G $，那么生成器在其上具有在$ \ Mathcal $ \ Mathcal {C} $上以适当富裕的$ \ Mathcal {c} $表达的本地属性，那么Markov流程会通过$ G $ G $ g $。结果适用于仅在$ \ MATHCAL {C} $上与生成器关联的任何Markov进程。这指出，该过程的路径连续性是由发电机在足够的测试功能上加密的先验属性，并且在许多情况下都可以轻松检查该属性。该方法使用潜在的理论工具，并涵盖与（可能是时间依赖的）二阶二级差异操作员（例如，通过Martingale问题）相关的Markov过程，该过程在Hilbert Space的域或度量空间上定义了。
We prove that if we are given a generator of a cadlag Markov process and an open domain $G$ in the state space, on which the generator has the local property expressed in a suitable way on a class $\mathcal{C}$ of test functions that is sufficiently rich, then the Markov process has continuous paths when it passes through $G$. The result holds for any Markov process which is associated with the generator merely on $\mathcal{C}$. This points out that the path continuity of the process is an a priori property encrypted by the generator acting on enough test functions, and this property can be easily checked in many situations. The approach uses potential theoretic tools and covers Markov processes associated with (possibly time-dependent) second order integro-differential operators (e.g., through the martingale problem) defined on domains in Hilbert spaces or on spaces of measures.
