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Mon, 03 Apr 2000 00:00:00 +0200Mon, 03 Apr 2000 00:00:00 +0200Smooth probability measures and associated differential operators
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/770
We compare different notions of differentiability of a measure along a vector field on a locally convex space. We consider in the L2-space of a differ entiable measure the analoga of the classical concepts of gradient, divergence and Laplacian (which coincides with the OrnsteinUhlenbeck operator in the Gaussian case). We use these operators for the extension of the basic results of Malliavin and Stroock on the smoothness of finite dimensional image measures under certain nonsmooth mappings to the case of non-Gaussian measures. The proof of this extension is quite direct and does not use any Chaos-decomposition. Finally, the role of this Laplacian in the procedure of quantization of anharmonic oscillators is discussed.O.G. Smolyanov; Heinrich von Weizsäckerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/770Mon, 03 Apr 2000 00:00:00 +0200Some reflections on and experiences with SPLIFS
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/771
Starting from the uniqueness question for mixtures of distributions this review centers around the question under which formally weaker assumptions one can prove the existence of SPLIFs, in other words perfect statistics and tests. We mention a couple of positive and negative results which complement the basic contribution of David Blackwell in 1980. Typically the answers depend on the choice of the set theoretic axioms and on the particular concepts of measurability.Heinrich von Weizsäckerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/771Mon, 03 Apr 2000 00:00:00 +0200Identifying a finite graph by its random walk
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/774
In the following we illustrate by two examples and simplify the statement of the main result of a joint paper with Peter ScheffelHeinrich von Weizsäckerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/774Mon, 03 Apr 2000 00:00:00 +0200