On Uniformly Subelliptic Operators and Stochastic Area

Details On Uniformly Subelliptic Operators and Stochastic Area On Uniformly Subelliptic Operators and Stochastic Area

2006-08-31

arxiv.org/abs/math/0609007v2

Mathematics

Probability

Scientific paper

We consider uniformly subelliptic operators on certain unimodular Lie groups of polynomial growth. It was shown by Saloff-Coste and Stroock that classical results of De Giorgi, Nash, Moser, Aronson extend to this setting. It was then observed by Sturm that many proofs extend naturally to the setting of locally compact Dirichlet spaces. We relate these results to what is known as rough path theory by showing that they provide a natural and powerful analytic machinery for construction and study of (random) geometric Hoelder rough paths. (In particular, we obtain a simple construction of the Lyons-Stoica stochastic area for a diffusion process with uniformly elliptic generator in divergence form.) Our approach then enables us to establish a number of far-reaching generalizations of classical theorems in diffusion theory including Wong-Zakai approximations, Freidlin-Wentzell sample path large deviations and the Stroock-Varadhan support theorem. The latter was conjectured by T. Lyons in his recent St. Flour lecture.

Affiliated with

Also associated with

No associations

Rating

On Uniformly Subelliptic Operators and Stochastic Area does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Uniformly Subelliptic Operators and Stochastic Area, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Uniformly Subelliptic Operators and Stochastic Area will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-492541