Existence and uniqueness results for time-inhomogeneous time-change equations and Fokker--Planck equations
arXiv:1812.08579 · doi:10.1007/s10959-019-00969-y
Abstract
We prove existence and uniqueness of solutions to Fokker--Planck equations associated to Markov operators multiplicatively perturbed by degenerate time-inhomogeneous coefficients. Precise conditions on the time-inhomogeneous coefficients are given. In particular, we do not necessarily require the coefficients to be neither globally bounded nor bounded away from zero. The approach is based on constructing random time-changes and studying related martingale problems for Markov processes with values in locally compact, complete and separable metric spaces.
This manuscript is mainly part of the preprint arXiv:1703.05673v1, which is now divided in two separate works