Renormalized BBM with rough Gaussian initial data converges in law to stochastic BBM forced by derivative of spatial white noise, for all regularities alpha <= 1/4.
Nelson, A quartic interaction in two dimensions , 1966 Mathematical Theory of Elementary Particles (Proc
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Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation
Renormalized BBM with rough Gaussian initial data converges in law to stochastic BBM forced by derivative of spatial white noise, for all regularities alpha <= 1/4.