Time-Homogeneous Parabolic Wick-Anderson Model in One Space Dimension: Regularity of Solution

摘要

Even though the heat equation with random potential is a well-studied object,the particular case of time-independent Gaussian white noise in one spacedimension has yet to receive the attention it deserves. The paper investigatesthe stochastic heat equation with space-only Gaussian white noise on a boundedinterval. The main result is that the space-time regularity of the solution isthe same for additive noise and for multiplicative noise in theWick-It\^o-Skorokhod interpretation.