Bismut’s Way of the Malliavin Calculus for Large Order Generators on a Lie Group †
Département de mathématiques, Université de Bourgogne-Franche-Comté, 25030 Besançon, France
†
Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017.
Proceedings 2018, 2(1), 82; https://doi.org/10.3390/proceedings2010082
Published: 5 January 2018
(This article belongs to the Proceedings of The First International Conference on Symmetry)
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/).
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MDPI and ACS Style
Léandre, R. Bismut’s Way of the Malliavin Calculus for Large Order Generators on a Lie Group. Proceedings 2018, 2, 82. https://doi.org/10.3390/proceedings2010082
AMA Style
Léandre R. Bismut’s Way of the Malliavin Calculus for Large Order Generators on a Lie Group. Proceedings. 2018; 2(1):82. https://doi.org/10.3390/proceedings2010082
Chicago/Turabian StyleLéandre, Rémi. 2018. "Bismut’s Way of the Malliavin Calculus for Large Order Generators on a Lie Group" Proceedings 2, no. 1: 82. https://doi.org/10.3390/proceedings2010082
