Rough evolution equations

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.

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)

References in corpus (1)

• Wiener chaos solutions of linear stochastic evolution equations

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