Strong Feller property via moment method

Published 26 May 2026 in math.PR | (2605.26439v1)

Abstract: This note studies the 1D stochastic heat equation driven by a one-dimensional Brownian motion. We prove that the associated Markov process satisfies the strong Feller property under mild non-degeneracy conditions. The approach combines Malliavin calculus with the moment method from PDE control theory.

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