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

2017/04/23 by Kim, Hyun-Jung, Lototsky, Sergey V
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1704.06995

Abstract

Even though the heat equation with random potential is a well-studied object, the particular case of time-independent Gaussian white noise in one space dimension has yet to receive the attention it deserves. The paper investigates the stochastic heat equation with space-only Gaussian white noise on a bounded interval. The main result is that the space-time regularity of the solution is the same for additive noise and for multiplicative noise in the Wick-Itô-Skorokhod interpretation.

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