Hitting properties of parabolic SPDE's with reflection

We study the hitting properties of the solutions u of a class of parabolic stochastic partial differential equations with singular drifts that prevent u from becoming negative. The drifts can be a reflecting term or a nonlinearity cu(-3), with c > 0. We prove that almost surely, for all time t > 0, the solution ut hits the level 0 only at a finite number of space points, which depends explicitly on c. In particular, this number of hits never exceeds 4 and if c > 15/8, then level 0 is not hit.