Controlled viscosity solutions of fully nonlinear rough PDEs

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

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

We propose a definition of viscosity solutions to fully nonlinear PDEs driven by a rough path via appropriate notions of test functions and rough jets. These objects will be defined as controlled processes with respect to the driving rough path. We show that this notion is compatible with the seminal results of Lions and Souganidis and with the recent results of Friz and coauthors on fully non-linear SPDEs with rough drivers.

Mots clés: Rough paths theory; Stochastic viscosity solutions; Stoch astic PDEs

Domaines: Probabilités [math.PR]

Massimiliano Gubinelli, Samy Tindel, Iván Torrecilla. Controlled viscosity solutions of fully nonlinear rough PDEs. [Research Report] non spécifié. 2014. ⟨hal-00958201⟩