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Large-time behavior for viscous and non-viscous Hamilton-Jacobi equations forced by additive noise
Nicolas Dirr and Panagiotis E. Souganidis
We study the large time behavior of the solutions to viscous and non-viscous Hamilton-Jacobi equations with additive noise and periodic spatial dependence. Under general structural conditions on the Hamiltonian, we show the existence of unique up to constants global in time solutions, which attract any other solution.