Rough evolution equations

Massimiliano Gubinelli (1) , Samy Tindel (2, 3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 IECN - Institut Élie Cartan de Nancy
3 BIGS - Biology, genetics and statistics

We show how to generalize Lyons' rough paths theory in order to give a pathwise meaning to some nonlinear infinite-dimensional evolution equations associated to an analytic semigroup and driven by an irregular noise. As an illustration, we apply the theory to a class of 1d SPDEs driven by a space-time fractional Brownian motion.

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Massimiliano Gubinelli, Samy Tindel. Rough evolution equations. Annals of Probability, 2010, 38, pp.1-75. ⟨10.1214/08-AOP437⟩. ⟨hal-00359724⟩