On \(\mathcal S\)-subordination and applications to entrance laws. (English) Zbl 1389.60092
Summary: Let \(\mathbb U\) and \(\mathbb V\) be two sub-Markovian resolvents of kernels such that \(\mathbb V\) is \(\mathcal S\)-subordinated to \(\mathbb U\), i.e., each \(\mathbb U\)-excessive function is \(\mathbb V\)-excessive. Based on results of J. Steffens [Math. Z. 210, No. 3, 495–512 (1992; Zbl 0770.60069)], we prove that the energy functional of \(\mathbb V\) is partially induced by the one of \(\mathbb U\) by some sort of projection. As application, we solve the so-called Bochner subordination problem for entrance laws in complete generality.
MSC:
60J35 | Transition functions, generators and resolvents |
60J40 | Right processes |
60J45 | Probabilistic potential theory |
31D05 | Axiomatic potential theory |