The Annals of Applied Probability

Large deviations for fast transport stochastic RDEs with applications to the exit problem

Sandra Cerrai and Nicholas Paskal

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We study reaction diffusion equations with a deterministic reaction term as well as two random reaction terms, one that acts on the interior of the domain, and another that acts only on the boundary of the domain. We are interested in the regime where the relative sizes of the diffusion and reaction terms are different. Specifically, we consider the case where the diffusion rate is much larger than the rate of reaction, and the deterministic rate of reaction is much larger than either of the random rate of reactions.

Article information

Ann. Appl. Probab., Volume 29, Number 4 (2019), 1993-2032.

Received: April 2018
Revised: September 2018
First available in Project Euclid: 23 July 2019

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Mathematical Reviews number (MathSciNet)

Primary: 60H15: Stochastic partial differential equations [See also 35R60] 70K65: Averaging of perturbations 60F10: Large deviations

Stochastic reaction–diffusion equations averaging principle large deviations exit problem Laplace principle


Cerrai, Sandra; Paskal, Nicholas. Large deviations for fast transport stochastic RDEs with applications to the exit problem. Ann. Appl. Probab. 29 (2019), no. 4, 1993--2032. doi:10.1214/18-AAP1439.

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