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A note on the strong Feller property via the moment method
Ziyu Liu, Shengquan Xiang · 2026-05-26 · via math updates on arXiv.org

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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