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.
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Heyer, H., Pap, G. Gaussian hemigroups on a locally compact group. Acta Mathematica Hungarica 103, 197–224 (2004). https://doi.org/10.1023/B:AMHU.0000028408.90695.59
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DOI: https://doi.org/10.1023/B:AMHU.0000028408.90695.59