Dominik Kortschak

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In this paper we extend some results about the probability that the sum of n dependent subex-ponential random variables exceeds a given threshold u. In particular, the case of non-identically distributed and not necessarily positive random variables is investigated. Furthermore we establish criteria how far the tail of the marginal distribution of an(More)
Notch encodes a transmembrane protein that functions in intercellular signaling. Although there is one Notch gene in Drosophila, vertebrates have three or more with overlapping patterns of embryonic expression. We cloned the entire 7575-bp coding region of an amphioxus Notch gene (AmphiNotch), encoding 2524 amino acids, and obtained the exon/intron(More)
For estimating P(<i>S</i><sub><i>n</i></sub> &gt; <i>x</i>) by simulation where <i>S</i><sub><i>k</i></sub> = <i>Y</i><sub>1</sub>+...+<i>Y</i><sub><i>k</i></sub> with <i>Y</i><sub>1</sub>, ...<i>, Y</i><sub><i>n</i></sub> are non-negative and heavy-tailed with distribution <i>F</i>, (Asmussen and Kroese 2006) suggested the estimator(More)
In this paper we propose a highly accurate approximation procedure for ruin probabilities in the classical collective risk model, which is based on a quadrature/rational approximation procedure proposed by Trefethen et al. [12]. For a certain class of claim size distributions (which contains the completely monotone distributions) we give a theoretical(More)
In the last decade considerable practical interest, e.g. in credit and insurance risk or telecommunication applications, as well as methodological challenges caused intensive research on estimation of rare event probabilities. This article aims to show that recently developed rare event estimators are especially well-suited for a quasi-Monte Carlo framework(More)
In the last decade considerable practical interest, e.g. in credit and insurance risk or telecommunication applications, as well as methodological challenges caused intensive research on estimation of rare event probabilities. This article aims to show that recently developed rare event estimators are especially well-suited for a quasi-Monte Carlo framework(More)
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