By constructing a coupling in two steps and using the Girsanov theorem under a regular conditional probability, the log-Harnack inequality is established for a large class of Gruschin type semigroups whose generator might be both degenerate and non-Lipschitz.
Cite this article
Feng-Yu Wang, Lihu Xu, Log-Harnack inequality for Gruschin type semigroups. Rev. Mat. Iberoam. 30 (2014), no. 2, pp. 405–418DOI 10.4171/RMI/786