Bismut’s Way of the Malliavin Calculus for Large Order Generators on a Lie Group

Rémi Léandre

doi:10.3390/proceedings2010082

Département de mathématiques, Université de Bourgogne-Franche-Comté, 25030 Besançon, France

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Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017.

Proceedings2018, 2(1), 82;https://doi.org/10.3390/proceedings2010082

This article belongs to the Proceedings The First International Conference on Symmetry

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We give an adaptation of the Malliavin Calculus of Bismut type in order to show that an operator of big order on a compact connected. Lie group is such that the associated semi-group has an heat-kernel. By mixing Wentzel-Freidlin estimates which were establised by us for non-markovian semi-groups and the Malliavin Calculus, we deduce logarithmic estimates of the heat-kernel in small time. We use deeply the symmetry of the group in the proof of the theorem.

© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Bismut’s Way of the Malliavin Calculus for Large Order Generators on a Lie Group^†

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Bismut’s Way of the Malliavin Calculus for Large Order Generators on a Lie Group^†