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PSF: Probability, Statistics and Financial Mathematics
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Invertible complex measures on Euclidian space 1: Technische Universität Dresden; 2: Universität Ulm In 1971, Taylor characterised all complex measures on the real line that are invertible with respect to convolution. We extend Taylor's result to complex measures on Euclidian space. Somewhat surprisingly, the structure of these measures turns out to be not much more complicated than in the one-dimensional case. The characterisation is via the characterisic function and it is shown that invertible complex measures must have a Levy-Khintchine-type representation with a signed Levy measure that satisfies some additional constraints. The study of invertible complex measures has some impact on the theory of quasi-infinitely probability distributions on Euclidian space. Rough differential equations driven by Besov-Orlicz paths 1: Charles University, Faculty of Mathematics and Physics, Czech Republic; 2: The Czech Academy of Sciences, Institute of Information Theory and Automation, Czech Republic The talk is devoted to path regularity of stochastic process and solutions to differential equations driven by them. It is well-known that a (fractional) Brownian motion has paths in a certain exponential Besov-Orlicz function space. We will present a generalization of this result to non-Gaussian stochastic processes and show that pathwise solutions to nonlinear differential equations driven by such processes retain the regularity of the driver both in the Young and rough regimes. Tackling the 6/49 Lottery and Debunking Common Myths with Probabilistic Methods and Combinatorial Designs Private Researcher, Germany At the end, the house always wins! This simple truth holds for all public games of chance. Nevertheless, since lotteries have existed, people have tried everything to give luck a helping hand. This presentation compares objective scientific approaches to tackle the 6/49 lottery: probabilistic methods and combinatorial designs. The mathematical models developed herein can be modified and applied to other lotteries. The newly constructed (49, 6, 5) covering design is introduced, which meets the Schönheim bound. It currently ranks among the largest and most efficient combinatorial designs made available for free download in the La Jolla Covering Repository. For lottery designs and for covering designs, a benchmark based on probabilistic methods is presented. It is demonstrated that common attempts to outwit the odds correspond to limitations of numbers to subsets, which disproportionately reduce the chances of winning. | ||
