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

Abstract

first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: Open AccessAbstract Bismut’s Way of the Malliavin Calculus for Large Order Generators on a Lie Group † by Rémi Léandre 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) Download Download PDF Download PDF with Cover Download XML Versions Notes 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/). Share and Cite 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 Style Léandre, 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 Find Other Styles Article Metrics No No Article Access Statistics Multiple requests from the same IP address are counted as one view.