Strong Feller property via moment method
Probability
2026-05-27 v1
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.
Cite
@article{arxiv.2605.26439,
title = {Strong Feller property via moment method},
author = {Ziyu Liu and Shengquan Xiang},
journal= {arXiv preprint arXiv:2605.26439},
year = {2026}
}