Moderate deviations for systems of slow–fast stochastic reaction–diffusion equations

@article{Gasteratos2020ModerateDF,
  title={Moderate deviations for systems of slow–fast stochastic reaction–diffusion equations},
  author={Ioannis Gasteratos and Michael Salins and Konstantinos V. Spiliopoulos},
  journal={Stochastics and Partial Differential Equations: Analysis and Computations},
  year={2020}
}
The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak convergence methods in infinite dimensions and related stochastic control arguments, we obtain an exact form for the moderate deviations rate function in different regimes as the small noise and time-scale separation parameters vanish. Many issues that come… 

Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime

A BSTRACT . We develop a provably efficient importance sampling scheme that estimates exit probabilities of so- lutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods

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