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This article studies a linear scalar delay differential equation subject tosmall multiplicative power tail L\'evy noise. We solve the first passage (theKramers) problem with probabilistic methods and discover an asymptotic loss ofmemory in this non-Markovian system. Furthermore, the mean exit time increasesas the power of the small noise amplitude, whereas the pre-factor accounts formemory effects. In particular, we discover a non-linear delay-induced exitacceleration due to a non-normal growth phenomenon. Our results are illustratedin the well-known linear delay oscillator driven by $\alpha$-stable L\'evyflights.

The first passage problem for stable linear delay equations perturbed by power law L\'evy noise