Stochastic calculus on foliations

• Grant number: 08/09120-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2009
• End date: January 31, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paulo Regis Caron Ruffino
• Grantee: Diego Sebastian Ledesma
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 07/06896-5 - Geometry of control, dynamical and stochastic systems, AP.TEM

Abstract

We shall study Markov semigroups generated by foliated diffusions, mainly unequalities relating curvature and dimensions, generalizing results by Ledoux. In the case of Markov semigroup generated by foliated Brownian motion, one expects to get equalities of this kind using foliated Bochner-Weintzenbock identity. We shall consider questions on regularity and ergodicity for harmonic measures as introduced by Lucy Garnett.