Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions
Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions
Abstract We study fully nonlinear second-order (forward) stochastic PDEs. They can also be viewed as forward path-dependent PDEs and will be treated as rough PDEs under a unified framework. For the most general fully nonlinear case, we develop a local theory of classical solutions and then define viscosity solutions through …