For SDEs on R^d, the paper proves existence and uniqueness of the optimal infinitesimal local kernel perturbation maximizing the linear response of an observable, and demonstrates a numerical approximation on a double-well example.
Extreme Value theory and Poisson statistics for discrete time samplings of stochastic differential equations
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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.
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Optimal response for stochastic differential equations by local kernel perturbations
For SDEs on R^d, the paper proves existence and uniqueness of the optimal infinitesimal local kernel perturbation maximizing the linear response of an observable, and demonstrates a numerical approximation on a double-well example.