Abstract
The stochastic nonlinear infinite-dimensional equations of gradient type and with additive Wiener noise can be reduced to an optimal convex control problem via Brezis–Ekeland duality device. This approach is illustrated here on a few classes of nonlinear stochastic parabolic equations which are relevant as diffusion models under stochastic Gaussian perturbations, and image restoring technique.
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Barbu, V. Optimal Control Approach to Nonlinear Diffusion Equations Driven by Wiener Noise. J Optim Theory Appl 153, 1–26 (2012). https://doi.org/10.1007/s10957-011-9946-8
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DOI: https://doi.org/10.1007/s10957-011-9946-8