# 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…

## One Citation

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## References

SHOWING 1-10 OF 35 REFERENCES

### Large deviations and averaging for systems of slow-fast stochastic reaction–diffusion equations

- MathematicsStochastics and Partial Differential Equations: Analysis and Computations
- 2019

We study a large deviation principle for a system of stochastic reaction–diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The…

### Large Deviations and Importance Sampling for Systems of Slow-Fast Motion

- Mathematics, Computer Science
- 2013

In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of…

### Normal deviations from the averaged motion for some reaction-diffusion equations with fast oscillating perturbation

- Mathematics
- 2009

### Large deviations and approximations for slow–fast stochastic reaction–diffusion equations

- Mathematics
- 2012

### Importance Sampling for Slow-Fast Diffusions Based on Moderate Deviations

- MathematicsMultiscale Model. Simul.
- 2020

We consider systems of slow-fast diffusions with small noise in the slow component. We construct provably logarithmic asymptotically optimal importance schemes for the estimation of rare events based…

### Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term

- Mathematics
- 2003

Abstract We study existence and uniqueness of a mild solution in the space of continuous functions and existence of an invariant measure for a class of reaction-diffusion systems on bounded domains…

### Large deviations for infinite dimensional stochastic dynamical systems

- Mathematics
- 2008

The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be…

### Averaging principle for a class of stochastic reaction–diffusion equations

- Mathematics
- 2008

We consider the averaging principle for stochastic reaction–diffusion equations. Under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow…

### Asymptotic behavior of multiscale stochastic partial differential equations

- Mathematics
- 2020

In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first…