## The Annals of Probability

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

### Rough evolution equations

Massimiliano Gubinelli and Samy Tindel

#### 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.