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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.

MSC:

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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References:

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