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On projective invariance of multi-parameter Brownian motion

Published online by Cambridge University Press:  22 January 2016

Shigeo Takenaka
Shigeo Takenaka*
Affiliation:
Department of Mathematics, Nagoya University
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The multi-parameter Brownian motion introduced by P. Lévy is not only a basic random field but also gives us interesting fine probabilistic structures as well as important properties from the view point of analysis. We shall be interested in investigation of such structures and properties by expressing the Brownian motion in terms of the multiparameter white noise. The expression naturally requires basic tools from analysis, in particular the Radon transform. While there arises the special linear group SL(n + 1, R), to which the Radon transform is adapted, and the group plays an important role in observing probabilistic structures of the Brownian motion. To be more interested, we can give some deep insight to unitary representations of SL(n + 1, R) through our discussion.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 67 , August 1977 , pp. 89 - 120
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

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