SPDE with generalized drift and fractional-type noise

  • Ciprian A. Tudor
  • Mounir Zili


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.


Stochastic partial differential equations Discontinuous drift Fractional Brownian motion Bifractional Brownian motion Stochastic heat equation Hölder continuity Wiener integral Covariance measure structure 

Mathematics Subject Classification

Primary 60F05 Secondary 60H05 91G70 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Laboratoire Paul PainlevéUniversité de Lille 1Villeneuve d’AscqFrance
  2. 2.Facultad de IngenieríaUniversidad de Valparaíso CIMFAVValparaisoChile
  3. 3.Department of Mathematics, Faculty of sciences of MonastirUniversity of MonastirMonastirTunisia

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