| Abstract: |
| We study moderate deviations for systems of slow-fast reaction-diffusion equations with space-time white noise on the fast component. In particular, we derive the corresponding Laplace principle via the weak convergence method which is based on a variational representation for functionals of the noise. The moderate deviations scaling and the infinite-dimensional nature of the problem necessitate a delicate approach to the proof of tightness of the related processes. The latter involves the solvability and regularity of solutions to Kolmogorov equations in Hilbert spaces and a finite-dimensional approximation argument which allows for an application of It\^o`s lemma. This is joint work with Michael Salins and Konstantinos Spiliopoulos. |
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