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math.PR2026
Asymptotic strong Feller and weak observability inequality
Ziyu Liu, Shengquan Xiang
For a class of non-autonomous linear SPDEs, we establish the equivalence among asymptotic regularization, weak observability, and approximate null controllability for the associate…
math.PR2026
A note on the strong Feller property via the moment method
Ziyu Liu, Shengquan Xiang
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 unde…
math.PR2026
Exponential mixing for the stochastic Allen--Cahn equation with localized white noise
Ziyu Liu, Shengquan Xiang, Zhifei Zhang
This paper studies the 1D stochastic Allen--Cahn equation on a bounded domain driven by localized white noise. We prove that the associated Markov process admits a unique invariant…