Moments of Brownian Motions on Lie Groups

• Autores: Michael Voit
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 145, Nº 3, 2005, págs. 247-260
• Idioma: inglés
• DOI: 10.1007/s00605-005-0312-5
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• Resumen

  • 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.