Extreme Value Theory and Poisson Statistics for Discrete Time Samplings of Stochastic Differential Equations

Abstract

We investigate the distribution and clustering of extreme events of 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 annealed transfer operators on suitable spaces of 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.