Long-time behaviour of degenerate diffusions: Ufg-type sdes and time-inhomogeneous hypoelliptic processes

We study the long time behaviour of a large class of diffusion processes on R^N, generated by second order differential operators of (possibly) degenerate type. The operators that we consider need not satisfy the Hörmander Condition (HC). Instead, they satisfy the so-called UFG condition, introduced by Herman, Lobry and Sussman in...