Rough evolution equations
Probability
2010-01-26 v2 Functional Analysis
Abstract
We generalize Lyons' rough paths theory in order to give a pathwise meaning to some nonlinear infinite-dimensional evolution equation associated to an analytic semigroup and driven by an irregular noise. As an illustration, we discuss a class of linear and nonlinear 1d SPDEs driven by a space--time Gaussian noise with singular space covariance and Brownian time dependence.
Keywords
Cite
@article{arxiv.0803.0552,
title = {Rough evolution equations},
author = {Massimiliano Gubinelli and Samy Tindel},
journal= {arXiv preprint arXiv:0803.0552},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.1214/08-AOP437 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)