Abstract
We consider a semilinear advection equation driven by a highly oscillatory space-time Gaussian random field, with the randomness affecting both the drift and the nonlinearity. In the linear setting, classical results show that the characteristics converge in distribution to a homogenized Brownian motion, hence, the pointwise law of the solution is close to a functional of the Brownian motion. Our main result is that the nonlinearity plays the role of a random diffeomorphism, and the pointwise limiting distribution is obtained by applying the diffeomorphism to the limit in the linear setting.
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