Titlebook: Extraction of Quantifiable Information from Complex Systems; Stephan Dahlke,Wolfgang Dahmen,Harry Yserentant Book 2014 Springer Internatio

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Book 2014 exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challeng

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Constructive Quantization and Multilevel Algorithms for Quadrature of Stochastic Differential Equattrajectory of a Lévy-driven SDE. We establish error estimates and central limit theorems for a multilevel Monte Carlo algorithm that achieves error rates of order . as the runtime . of the algorithm tends to infinity.

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Robustness in Stochastic Filtering and Maximum Likelihood Estimation for SDEs,e of affairs for users who effectively face an ill-posed situation: close observations may lead to vastly different predictions. A similar question can be asked in the context of (maximum likelihood) parameter estimation for diffusions. Some (apparently novel) counter examples show that, here again,

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Information and Its Role in Naturege in ... Moreover, in the context of parameter dependent problems we discuss two approaches serving different purposes and working under different regularity assumptions. For “frequent query problems”, making essential use of the novel well-conditioned variational formulations, a new . is outlined

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Channel Capacity and Channel Codingroblems on . with random right-hand side. Such problems appear naturally when applying Rothe’s method to the parabolic stochastic equation. A general stochastic wavelet model for the right-hand side is introduced and its Besov regularity as well as linear and nonlinear approximation is studied. The