Hypoelliptic non-homogeneous diffusions

 Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} be a time dependent second order operator, written in usual or Hörmander form. We study the regularity of the law of the associated non-homogeneous (time dependent) diffusion process, under Hörmander's like conditions. Coefficients are only Hölder continuous in time. The main tool is Malliavin calculus. Our results extend and correct previous ones ([17] and related works, [15]). Related topics like filtering theory, killed or reflected processes, parabolic hypoellipticity are also discussed.