Rough evolution equations

Details Rough evolution equations Rough evolution equations

2008-03-04

arxiv.org/abs/0803.0552v2

Annals of Probability 2010, Vol. 38, No. 1, 1-75

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AOP437 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/08-AOP437

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.

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