Unique Continuation for Stochastic Hyperbolic Equations
Qi Lu, Zhongqi Yin
TL;DR
This paper establishes a local unique continuation property for stochastic hyperbolic equations using a global Carleman estimate, advancing the understanding of stochastic PDEs without boundary conditions.
Contribution
It introduces a novel approach to prove unique continuation for stochastic hyperbolic equations without boundary conditions using Carleman estimates.
Findings
Proved local unique continuation property for stochastic hyperbolic equations.
Developed a global Carleman estimate applicable to stochastic PDEs.
Extended the theory of unique continuation to stochastic settings.
Abstract
In this paper, we derive a local unique continuation property for stochastic hyperbolic equations without boundary conditions. This result is proved by a global Carleman estimate.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Numerical methods in inverse problems · Stochastic processes and financial applications