A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a probabilistic interpretation is investigated.
"Some parabolic PDEs whose drift is an irregular random noise in space." Ann. Probab. 35 (6) 2213 - 2262, November 2007. https://doi.org/10.1214/009117906000001178