Sebastian Krumscheid

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We consider the numerical approximation of a risk-averse optimal control problem for an elliptic partial differential equation (PDE) with random coefficients. Specifically, the control function is a deterministic, dis- tributed forcing term that minimizes ...

In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo (MLMC) estimators and we provide near optimal weaker conditions under which the CLT is achieved. In ...

We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to observations of the model ...

Many applications across sciences and technologies require a careful quantification of nondeterministic effects to a system output, for example, when evaluating the system’s reliability or when gearing it towards more robust operation conditions. At the he ...

In many physical, technological, social, and economic applications, one is commonly faced with the task of estimating statistical properties, such as mean first passage times of a temporal continuous process, from empirical data (experimental observations) ...

In this work we introduce and analyze a novel multilevel Monte Carlo (MLMC) estimator for the accurate approximation of central moments of system outputs affected by uncertainties. Central moments play a central role in many disciplines to characterize a r ...

In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential models by the MLM ...

Sebastian Krumscheid

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MATHICSE Technical Report : Analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Central limit theorems for multilevel Monte Carlo methods

Perturbation-based inference for diffusion processes: Obtaining effective models from multiscale data

Multilevel Monte Carlo Approximation of Functions

Data-driven coarse graining in action: Modeling and prediction of complex systems

Quantifying uncertain system outputs via the multilevel Monte Carlo method — Part I: Central moment estimation

Quantifying uncertain system outputs via the multi-level Monte Carlo method --- distribution and robustness measures