Fully nonlinear stochastic partial differential equations. (English. Abridged French version) Zbl 1002.60552

Lions, Pierre-Louis; Souganidis, Panagiotis E.

C. R. Acad. Sci., Paris, Sér. I, Math. 326, No. 9, 1085-1092 (1998).

Summary: In this Note, we propose a new theory of “stochastic viscosity solutions” for fully nonlinear stochastic partial differential equations. This theory allows to handle a large class of equations which covers in particular various applications such as models of phase transitions and front propagation in random media and pathwise stochastic control. These applications will be detailed in a subsequent note.

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
35K55	Nonlinear parabolic equations
35R60	PDEs with randomness, stochastic partial differential equations