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Posterior Consistency for Recovering Initial States in Nonlinear Subdiffusion Equations
We study the Bayesian recovery of the initial state in a semilinear time-fractional subdiffusion equation from noisy random space-time point observations. A rescaled Gaussian prior based on a Whittle--Matérn process is assigned to the unknown initial condition. We prove the \(H^{2+κ}\)-regularity of
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