Subordination in the Sense of Bochner of LP-semigroups and Associated Markov Processes

我们证明隶属在一个 L p 空格由 sub-Markovian 操作符的 C 0-semigroup 的卷绕旋转 semigroup (在 Bochner 的意义的隶属) 导致了实际上被联系到权利(Markov ) 的隶属进程。作为后果，我们与 L p 解决鞅问题伙伴辅助 semigroup 的无穷小的生成器。我们也为辅助 semigroup 的 L p 发电机的领域的元素证明伪连续性性质。结果基础空间的增大是必要的。在证明的主要的步是在是一个 Borel 正确过程的一个 Markov 过程的性质的如此的隶属下面的保藏。我们使用几个分析、概率的潜在的理论工具。

We show that the subordination induced by a convolution semigroup （subordi- nation in the sense of Bochner） of a C0-semigroup of sub-Markovian operators on an Lp space is actually associated to the subordination of a right （Markov） process. As a consequence, we solve the martingale problem associate with the LP-infinitesimal generator of the subordinate semigroup. We also prove quasi continuity properties for the elements of the domain of the LP-generator of the subordinate semigroup. It turns out that an enlargement of the base space is necessary. A main step in the proof is the preservation under such a subordination of the prop erty of a Markov process to be a Borel right process. We use several analytic and probabilistic potential theoretical tools.