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Gaussian hemigroups on a locally compact group |
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| Authors: | Herbert Heyer Gyula Pap |
| Institution: | (1) Mathematisches Institut, Universitát Tübingen, Auf Der Morgenstelle 10, D-72076 Tübingen, Germany;(2) Institute of Mathematics, University Of Debrecen, H-4010 Debrecen, Hungary |
| Abstract: | A notion of Gaussian hemigroup is introduced and its relationship with the Gauss condition is studied. Moreover, a Lévy-type martingale characterization is proved for processes with independent (not necessarily stationary) increments satisfying the Gauss condition in a compact Lie group. The characterization is given in terms of a faithful finite dimensional representation of the group and its tensor square. For the proofs noncommutative Fourier theory is applied for the convolution hemigroups associated with the increment processes. This revised version was published online in June 2006 with corrections to the Cover Date. |
| Keywords: | diffusion and Gaussian hemigroups Gauss condition convolution hemigroups and evolution operator families of finite variation martingale characterization convolution semigroups and hemigroups of probability measures increment processes |
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