Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance

Details Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance

2011-03-16

arxiv.org/abs/1103.3188v2

Mathematics

Probability

This is a replacement for a previously uploaded preprint

Scientific paper

We study the problem of non-asymptotic deviations between a reference measure and its empirical version, in the 1-Wasserstein metric, under the standing assumption that the measure satisfies a transport-entropy inequality. We extend some results of F. Bolley, A. Guillin and C. Villani with simple proofs. Our methods are based on concentration inequalities and extend to the general setting of measures on a Polish space. Deviation bounds for the occupation measure of a Markov chain are also given, under the assumption that the chain is contractive on the space of Lipschitz functions. Throughout the text, several examples are worked out, including the cases of Gaussian measures on separable Banach spaces, and laws of diffusion processes.

Affiliated with

Also associated with

No associations

Rating

Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance 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 Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-263346