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PSF: Probability, Statistics and Financial Mathematics Location: D301 Session Chair: Michael Kupper Session Chair: Mathias Trabs | |
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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. | |
