Explore extreme event distributions and multiple occurrences in stochastic processes derived from Stochastic Differential Equation solutions on R^n. Delve into the analysis of annealed transfer operators acting on probability density spaces, combining SDE theory with functional analytic approaches to dynamical systems. Learn about the spectral properties of these operators and their implications for extreme value theory and Poisson statistics. This 49-minute conference talk, presented at the Workshop on "Rare Events in Dynamical Systems" at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), offers insights into cutting-edge research conducted in collaboration with F. Flandoli, S. Galatolo, and P. Giulietti.