Abstract
We consider a stochastic partial differential equation involving a second order differential operator whose drift is discontinuous. The equation is driven by a Gaussian noise which behaves as a Wiener process in space and the time covariance generates a signed measure. This class includes the Brownian motion, fractional Brownian motion and other related processes. We give a necessary and sufficient condition for the existence of the solution and we study the path regularity of this solution.
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Tudor, C.A., Zili, M. SPDE with generalized drift and fractional-type noise. Nonlinear Differ. Equ. Appl. 23, 53 (2016). https://doi.org/10.1007/s00030-016-0407-9
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DOI: https://doi.org/10.1007/s00030-016-0407-9