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arXiv · 2009.08418

Regularisation by regular noise

Máté Gerencsér
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Abstract

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 $\alpha>1-1/(2H)$ is recovered for all non-integer $H>1$.

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Máté Gerencsér. 2020-09-17. Regularisation by regular noise. https://doi.org/10.1007/s40072-022-00242-0

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