5 papers
Unique Continuation Property for Stochastic Wave Equations
Qi Lü, Zhonghua Liao
This paper establishes a fundamental and surprising phenomenon in the theory of stochastic wave equations: the restoration of the unique continuation property (UCP) across characte…
Exact Controllability for a Refined Stochastic Hyperbolic Equation with Internal Controls
Zengyu Li, Zhonghua Liao, Qi Lü
We establish the internal exact controllability of a refined stochastic hyperbolic equation by deriving a suitable observability inequality via Carleman estimates for the associate…
On Inverse Problems for Mean Field Games with Common Noise via Carleman Estimate
Qi Lü, Zhonghua Liao
In this paper, we study two kinds of inverse problems for Mean Field Games (MFGs) with common noise. Our focus is on MFGs described by a coupled system of stochastic Hamilton-Jacob…
Stability Estimate for an Inverse Stochastic Parabolic Problem of Determining Unknown Time-varying Boundary
Zhonghua Liao, Qi Lü
Stochastic parabolic equations are widely used to model many random phenomena in natural sciences, such as the temperature distribution in a noisy medium, the dynamics of a chemica…
Exact controllability for a refined Stochastic Wave Equation
Zhonghua Liao, Qi Lü
In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-li…