Talagrand Concentration Inequalities for Stochastic Partial Differential Equations
Probability
2018-11-28 v3
Abstract
One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely continuous measure with finite relative entropy. Such transportation-information inequalities were recently established for some stochastic differential equations. Here, we develop a similar theory for some stochastic partial differential equations.
Cite
@article{arxiv.1709.07098,
title = {Talagrand Concentration Inequalities for Stochastic Partial Differential Equations},
author = {Davar Khoshnevisan and Andrey Sarantsev},
journal= {arXiv preprint arXiv:1709.07098},
year = {2018}
}
Comments
19 pages. Keywords: Stochastic partial differential equations, stochastic heat equation, stochastic fractional heat equation, concentration of measure, transportation-information inequality, relative entropy, Wasserstein distance