Abstract

In the present talk, I briefly explain the main analytical results of my PhD thesis: “Weak regularisation by degenerate Lévy noise and its applications”. In particular, I will show the Schauder estimates, a useful analytical tool for the well-posedness of SDEs, for two different classes of integro-differential equations whose coefficients lie in suitable anisotropic Hölder spaces with multi-indices of regularity. The first result focuses on parabolic operators with non-linear drift, when the main part is an α-stable operator acting only on the first component. To deal with the non-linear drift, some new controls on Besov norms are also presented. As an extension of the first one, I will then show the Schauder estimates for degenerate Ornstein-Uhlenbeck operators driven by a larger class of possibly asymmetric stable-like operators, such as the relativistic, layered or Lamperti stable ones.