Smooth probability measures and associated differential operators

  • 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.

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Metadaten
Author:O.G. Smolyanov, Heinrich von Weizsäcker
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7398
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Source:Inf. Dim. Analysis, Qunatum Prob. Rel. Topics, vol 2, 1998
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

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