Rough Paths and applications to support theorems

After a brief introduction to the basics of Rough Paths I'll

explain recent work by Peter Friz, Dan Stroock and myself proving that a

Brownian path conditioned to be uniformly close to a given smooth path

converges in distribution to that path in the Rough Path metric. The Stroock

Varadhan support theorem is an immediate consequence.

The novel part of the argument is to

obtain the estimate in a way that is independent of the particular norm used

in the Euclidean space when one defines the uniform norm on path space.