2014/03/12 by Massimiliano Gubinelli, Gubinelli, Massimiliano, Samy Tindel +3
Economics, Econometrics and Finance · Engineering · #Economic theories and models #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1403.2832
openalex publication_date 2014/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.