Subordination in the sense of Bochner of L (p) -semigroups and associated Markov processes

作者：Lupascu Oana^*

来源：Acta Mathematica Sinica-English Series, 2014, 30(2): 187-196.

DOI：10.1007/s10114-014-2751-1

• Subordination in the sense of Bochner
• L-p-semigroup
• subordinator
• right (Markov) process
• nonbranch point

We show that the subordination induced by a convolution semigroup (subordination in the sense of Bochner) of a C (0)-semigroup of sub-Markovian operators on an L (p) space is actually associated to the subordination of a right (Markov) process. As a consequence, we solve the martingale problem associate with the L (p) -infinitesimal generator of the subordinate semigroup. We also prove quasi continuity properties for the elements of the domain of the L (p) -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 property of a Markov process to be a Borel right process. We use several analytic and probabilistic potential theoretical tools.

• 出版日期2014-2