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We consider delay differential equations (DDE) that are on the verge of aninstability, i.e. the characteristic equation for the linearized equation hasone root as zero and all other roots have negative real parts. In presence ofsmall mean-zero noise, we study the large deviations from the correspondingdeterministic system. Using spectral theory for DDE it is easy to see that, theprojection on to the one dimensional space corresponding to the zero root isexponentially equivalent with the original process. For the one-dimensionalprocess we make the observation that the results of Freidlin-Wentzell apply.

Large deviations in presence of small noise for delay differential equations at an instability