Rough evolution equations

Massimiliano Gubinelli and Samy Tindel

First issued 4 March 2008 · PDF

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.

Versions

1. Version 2 (arXiv v2) current
   26 January 2010
   arXiv 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)
   PDF · sources not available: the source of this version is withheld on arXiv · files and digests · arXiv:0803.0552
2. Version 1 (arXiv v1)
   4 March 2008
   arXiv comments: 56 pages
   PDF · LaTeX source · files and digests · arXiv:0803.0552

Cite

Massimiliano Gubinelli and Samy Tindel. Rough evolution equations. Papers of Massimiliano Gubinelli, 2008, version 2. https://mgubi.org/papers/paper/rough-evolution-equations/

Licence: arXiv.org perpetual, non-exclusive license to distribute; all other rights reserved to the authors

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