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

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

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

Dynamical Systems 2024-03-20 v2 Probability

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

Abstract

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.

Keywords

extreme value theory poisson statistics stochastic differential equations discrete time sampling transfer operators annealed operators

Cite

@article{arxiv.2310.13972,
  title  = {Extreme Value theory and Poisson statistics for discrete time samplings of stochastic differential equations},
  author = {F. Flandoli and S. Galatolo and P. Giulietti and S. Vaienti},
  journal= {arXiv preprint arXiv:2310.13972},
  year   = {2024}
}

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

Abstract

Keywords

Cite

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