Moments of Brownian Motions on Lie Groups |
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Authors: | Michael Voit |
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Affiliation: | (1) Universität Dortmund, Germany |
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Abstract: | Let (Bt)t ≥ 0 be a Brownian motion on with the corresponding Gaussian convolution semigroup (μt)t ≥ 0 and generator L. We show that algebraic relations between L and the generators of the matrix semigroups lead to for t → s, k ≥ 1, and all coordinates i,j. These relations will form the basis for a martingale characterization of (Bt)t ≥ 0 in terms of generalized heat polynomials. This characterization generalizes a corresponding result for the Brownian motion on in terms of Hermite polynomials due to J. Wesolowski and may be regarded as a variant of the Lévy characterization without continuity assumptions. |
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Keywords: | 2000 Mathematics Subject Classifications: 60J65 60G44 60B15 22D20 |
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