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

2023/10/21 by Flandoli, F., Galatolo, S., Giulietti, P. +1 · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2310.13972

Abstract

We investigate the distribution and multiple occurrences of extreme events stochastic processes constructed by sampling the solution of a Stochastic Differential Equation on ℝⁿ. 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.

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