Open Access
January 2010 Rough evolution equations
Massimiliano Gubinelli, Samy Tindel
Ann. Probab. 38(1): 1-75 (January 2010). DOI: 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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Massimiliano Gubinelli. Samy Tindel. "Rough evolution equations." Ann. Probab. 38 (1) 1 - 75, January 2010.


Published: January 2010
First available in Project Euclid: 25 January 2010

zbMATH: 1193.60070
MathSciNet: MR2599193
Digital Object Identifier: 10.1214/08-AOP437

Primary: 60G15 , 60H05 , 60H07

Keywords: fractional Brownian motion , Rough paths theory , stochastic PDEs

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 1 • January 2010
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