Extreme Value theory and Poisson statistics for discrete time samplings of stochastic differential equations

F. Flandoli, S. Galatolo, P. Giulietti, S. Vaienti

Published 2023-10-21Version 1

We investigate the distribution and multiple occurrences of extreme events stochastic processes constructed by sampling the solution of a Stochastic Differential Equation on $\mathbb{R}^n$. We do so by studying the action of an annealead transfer operators on ad-hoc spaces of probability densities. The spectral properties of such operators are obtained by employing a mixture of techniques coming from SDE theory and a functional analytic approach to dynamical systems.