Abstract
We give a brief introduction and overview of the topic of regularization and well-posedness by noise for ordinary and partial differential equations. The article is an attempt to outline in a concise fashion different directions of research in this field that have attracted attention in recent years. We close the article with a look on more recent developments in the field of nonlinear SPDE, focusing on stochastic scalar conservation laws and porous media equations. The article is tailored at master/PhD level, trying to allow a smooth introduction to the subject and pointing at a large list of references to allow further in-depth study.
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