Optimal low-rank approximations to the posterior mean (with fixed covariance) and joint mean-covariance are derived for linear Gaussian inverse problems on separable Hilbert spaces, with equivalence conditions and projector interpretations.
An introduction to stochastic PDEs
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In infinite spin systems with noise on a single particle, unique invariant and periodic measures exist on finite subsystems and extend to the full lattice via tightness and weak convergence.
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Optimal low-rank posterior mean and distribution approximation in linear Gaussian inverse problems on Hilbert spaces
Optimal low-rank approximations to the posterior mean (with fixed covariance) and joint mean-covariance are derived for linear Gaussian inverse problems on separable Hilbert spaces, with equivalence conditions and projector interpretations.
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Invariant and periodic measures in classical spin systems on infinite lattices with highly degenerate noise
In infinite spin systems with noise on a single particle, unique invariant and periodic measures exist on finite subsystems and extend to the full lattice via tightness and weak convergence.
- Exponential integrability of the solution to the stochastic Burgers equation driven by white noise