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We consider a tree-based discretization technique utilizing conditional transportation distance, which is well suited for the approximation of multi-stage stochastic programming problems, and investigate corresponding convergence properties. We explain the relation between the approximation quality of the probability model and the quality of the solution.(More)
The flow of natural gas within a gas transmission network is studied with the aim to optimise such networks. The analysis of real data provides a deeper insight into the behavior of gas in-and outflow. A geoadditive model for describing the dependence between the maximum daily gas flow and the temperature on network exits is proposed. Semiparametric(More)
Positivity and positive definiteness in algebra of generalized functions are studied. Basic definitions and notions of Colombeau algebra of generalized functions are given and some special classes of positive definite generalized functions on those algebras are introduced. Their relation to distributions is also investigated.
The flow of natural gas within a gas transmission network is studied with the aim to predict gas loads for very low temperatures. Two models for describing dependence between the maximal daily gas flow and the temperature on network exits are presented. A Brain-Cousens regression model is chosen from the class of parametric models. As an alternative, a(More)
In this chapter we describe an approach for the statistical analysis of gas demand data. The objective is to model temperature dependent univariate and multivariate distributions allowing for later evaluation of network constellations with respect to the probability of demand satisfaction. In the first part, method-ologies of descriptive data analysis(More)
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