Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift

We consider Kolmogorov-Fokker-Planck equations with unbounded drift terms which are only measurable in time and locally Holder continuous in space. In particular, we extend the parametrix method to this setting and we prove existence and uniqueness of measure solutions to the associated Cauchy problem, as well as the equivalence with the corresponding stochastic formulation. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).