Rough evolution equations

Massimiliano Gubinelli; Samy Tindel

doi:10.1214/08-AOP437

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Home > Journals > Ann. Probab. > Volume 38 > Issue 1 > Article

January 2010 Rough evolution equations

Massimiliano Gubinelli, Samy Tindel

Ann. Probab. 38(1): 1-75 (January 2010). DOI: 10.1214/08-AOP437

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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.