Some parabolic PDEs whose drift is an irregular random noise in space. (English) Zbl 1147.60042

The authors consider a random partial differential equation of parabolic type with irregular noise in the drift, not necessarily Gaussian. Actually it is a new type of SPDE that is motivated by random irregular media models. They freeze a realization of the drift and then they are able to study the existence, uniqueness and probabilistic interpretation of the associated parabolic equation. They give a meaning to the solution using a martingale problem and as a stochastic differential equation (in a weak and in a strong sense). In order to obtain these results the authors make use of Young integrals and stochastic calculus via regularization.


60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
60G48 Generalizations of martingales
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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