Agnès Lagnoux

Rare Event Simulation

This article deals with estimations of probabilities of rare events using fast simulation based on the splitting method. In this technique, the sample paths are split into multiple copies at various stages in the simulation. Our aim is to optimize the algorithm and to obtain a precise confidence interval of the estimator using branching processes. The numerical results presented suggest that the method is reasonably efficient.

Sensitivity analysis for multidimensional and functional outputs

Let

Multilevel branching splitting algorithm for estimating rare event probabilities

X:=(X_1, \ldots, X_p)

Cross-validation estimation of covariance parameters under fixed-domain asymptotics

be random objects (the inputs), defined on some probability space

Statistical significance based on length and position of the local score in a model of i.i.d. sequences

(\Omega,{\mathcal{F}}, \mathbb P)

Asymptotic normality and efficiency of two Sobol index estimators

and valued in some measurable space

Sensitivity indices for multivariate outputs

E=E_1\times\ldots \times E_p

Estimation of the Sobol indices in a linear functional multidimensional model

. Further, let

Sensitivity Analysis Based on Cramér--von Mises Distance

Y:=Y = f(X_1, \ldots, X_p)

Probability that the maximum of the reflected Brownian motion over a finite interval

be the output. Here,