Harnack inequalities for stochastic heat equation with locally unbounded drift (Q2006732)

This paper is concerned with the Harnack inequalities for the stochastic heat equation with the Neumann boundary condition and the additive white noise in one dimension. For the corresponding Markov operator, the authors first prove the Harnack inequality, based on the coupling by change of measure and Krylov's estimate. Then they prove the shift (log-)Harnack inequality. Moreover, the application to the equivalence between the corresponding distributions of solutions is also obtained.