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Eikonal equations and pathwise solutions to fully non-linear SPDEs

Friz, Peter K.; Gassiat, Paul; Lions, Pierre-Louis; Souganidis, Panagiotis E.

We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Riemannian geometry. The results are new and extend the class of equations studied so far by the last two authors.
Published in: Stochastics and partial differential equations: analysis and computations, 10.1007/s40072-016-0087-9, Springer