Transportation-cost inequalities for nonlinear Gaussian functionals

In this talk, we study concentration properties for laws of non-linear Gaussian functionals on metric spaces. Our focus lies on measures with non-Gaussian tail behaviour which are beyond the reach of Talagrand’s classical Transportation – Cost Inequalities (TCIs). Motivated by solutions of Rough Differential Equations and relying on a suitable contraction principle, we prove generalised TCIs for functionals that arise in the theory of regularity structures and, in particular, in the cases of rough volatility and the two-dimensional Parabolic Anderson Model. Our work also extends existing results on TCIs for diffusions driven by Gaussian processes. This is joint work with Antoine Jacquier.

The talk will be followed by refreshments in the common room at 4pm.