Strong invariance and noise-comparison principles for some parabolic   stochastic PDEs
  We consider a system of interacting diffusions on the integer lattice. By letting the mesh size go to zero and by using a suitable scaling, we show that the system converges (in a strong sense) to a solution of the stochastic heat equation on the real line. As a consequence, we obtain comparison inequalities for product moments of the stochastic heat equation with different nonlinearities. 
Mathew Joseph, Davar Khoshnevisan, Carl Mueller
math.PR