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Stochastic calculus on foliations

Grant number: 08/09120-0
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): March 01, 2009
Effective date (End): January 31, 2010
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Paulo Regis Caron Ruffino
Grantee:Diego Sebastian Ledesma
Home 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.