  We consider the stationary O'Connell-Yor model of semi-discrete directed
polymers in a Brownian environment in the intermediate disorder regime and show
convergence of the increments of the log-partition function to the energy
solutions of the stochastic Burgers equation. The proof does not rely on the
Cole-Hopf transform and avoids the use of spectral gap estimates for the
discrete model. The key technical argument is a second-order Boltzmann-Gibbs
principle.
