Entropic Measure and Wasserstein Diffusion

Details Entropic Measure and Wasserstein Diffusion Entropic Measure and Wasserstein Diffusion

2007-04-05

arxiv.org/abs/0704.0704v1

Mathematics

Probability

Scientific paper

We construct a new random probability measure on the sphere and on the unit interval which in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It satisfies a quasi-invariance formula with respect to the action of smooth diffeomorphism of the sphere and the interval respectively. The associated integration by parts formula is used to construct two classes of diffusion processes on probability measures (on the sphere or the unit interval) by Dirichlet form methods. The first one is closely related to Malliavin's Brownian motion on the homeomorphism group. The second one is a probability valued stochastic perturbation of the heat flow, whose intrinsic metric is the quadratic Wasserstein distance. It may be regarded as the canonical diffusion process on the Wasserstein space.

Affiliated with

Also associated with

No associations

Rating

Entropic Measure and Wasserstein Diffusion 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 Entropic Measure and Wasserstein Diffusion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Entropic Measure and Wasserstein Diffusion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-293292