The Annals of Probability

Rough evolution equations

Massimiliano Gubinelli and Samy Tindel

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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.

Article information

Source
Ann. Probab. Volume 38, Number 1 (2010), 1-75.

Dates
First available in Project Euclid: 25 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1264433992

Digital Object Identifier
doi:10.1214/08-AOP437

Mathematical Reviews number (MathSciNet)
MR2599193

Zentralblatt MATH identifier
1193.60070

Subjects
Primary: 60H05: Stochastic integrals 60H07: Stochastic calculus of variations and the Malliavin calculus 60G15: Gaussian processes

Keywords
Rough paths theory stochastic PDEs fractional Brownian motion

Citation

Gubinelli, Massimiliano; Tindel, Samy. Rough evolution equations. Ann. Probab. 38 (2010), no. 1, 1--75. doi:10.1214/08-AOP437. https://projecteuclid.org/euclid.aop/1264433992.


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