Linear response formulas are established for invariant densities and observables of perturbed SDEs on the torus, followed by existence, uniqueness, and explicit characterization of optimal drift perturbations that maximize first-order observable variation, with Fourier numerics demonstrated in low-
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Derives explicit Lipschitz stability estimates for simultaneous recovery of density coefficient and initial displacement in a damped biharmonic wave equation from boundary measurements of Δu and its normal derivative.
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Optimal response for stochastic differential equations in $\mathbb{T}^d$ with perturbations on the drift term
Linear response formulas are established for invariant densities and observables of perturbed SDEs on the torus, followed by existence, uniqueness, and explicit characterization of optimal drift perturbations that maximize first-order observable variation, with Fourier numerics demonstrated in low-
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Lipschitz Stability for an Inverse Problem of Biharmonic Wave Equations with Damping
Derives explicit Lipschitz stability estimates for simultaneous recovery of density coefficient and initial displacement in a damped biharmonic wave equation from boundary measurements of Δu and its normal derivative.