Proves that E[exp(λ sup_t ||X_t^x||_L2^2)] is finite for the stochastic Burgers equation driven by (-Δ)^γ dW with γ < 1/4 using Boué-Dupuis and Da Prato-Debussche methods.
An introduction to stochastic PDEs
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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.
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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Exponential integrability of the solution to the stochastic Burgers equation driven by white noise
Proves that E[exp(λ sup_t ||X_t^x||_L2^2)] is finite for the stochastic Burgers equation driven by (-Δ)^γ dW with γ < 1/4 using Boué-Dupuis and Da Prato-Debussche methods.
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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.