Gerencser, M. (2023). Regularisation by regular noise. Stochastics and Partial Differential Equations: Analysis and Computations, 11, 714–729. https://doi.org/10.1007/s40072-022-00242-0
We show that perturbing ill-posed differential equations with (potentially very) smooth random processes can restore well-posedness—even if the perturbation is (potentially much) more regular than the drift component of the solution. The noise considered is of fractional Brownian type, and the familiar regularity condition α > 1 - 1 / (2 H) is recovered for all non-integer H > 1.
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