Aug 14, 2020 · We prove an error bound for the approximation error of the probability of failure, which behaves like the discretization accuracy of the PDE multiplied by an ...

We consider failure events that are expressed in terms of a limit-state function, which depends on the solution of a partial differential equation (PDE).

Jun 18, 2021 · Abstract. The estimation of the probability of rare events is an important task in reliabil- ity and risk assessment.

Jul 15, 2021 · Abstract. The estimation of the probability of rare events is an important task in reliability and risk assessment.

In this paper, we consider the estimation of ruin probability in the classical compound Poisson model. We first show that the ruin probability can be expressed ...

Error analysis for probabilities of rare events with approximate models · Fabian Wagner, J. Latz, +1 author. E. Ullmann · Published in SIAM Journal on Numerical…

Aug 14, 2020 · In many applications, the PDE cannot be solved analytically. We can only evaluate an approximation of the exact PDE solution. Therefore, the ...

To compute the rare-event (failure) probability for a dynamic system, both input (excitation) and modeling uncertainties should be quantified and propagated.

Conclusions: Calculating the probability of observing a small number of events using standard approaches may result in substantial errors.

Abstract. We are interested in estimating probabilities of rare events in the context of com- puter experiments. These rare events depend on the output of a ...