Controlled viscosity solutions of fully nonlinear rough PDEs

Torrecilla, Iván; Tindel, Samy; Gubinelli, Massimiliano

Torrecilla, Iván; Tindel, Samy; Gubinelli, Massimiliano (2014), Controlled viscosity solutions of fully nonlinear rough PDEs. https://basepub.dauphine.fr/handle/123456789/12904

Type

Document de travail / Working paper

External document link

http://hal.archives-ouvertes.fr/hal-00958201

Date

2014

Publisher

Université Paris-Dauphine

Published in

Paris

Metadata

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Author(s)

Torrecilla, Iván
Tindel, Samy
Gubinelli, Massimiliano

Abstract (EN)

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.

Subjects / Keywords

Stochastic PDEs; Stochastic viscosity solutions; Rough paths theory