Large-Time Behavior for Viscous and Nonviscous Hamilton-Jacobi Equations Forced by Additive Noise

@article{Dirr2005LargeTimeBF,
  title={Large-Time Behavior for Viscous and Nonviscous Hamilton-Jacobi Equations Forced by Additive Noise},
  author={Nicolas Dirr and Panagiotis E. Souganidis},
  journal={SIAM J. Math. Analysis},
  year={2005},
  volume={37},
  pages={777-796}
}
We study the large-time behavior of the solutions to viscous and nonviscous 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. 
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