A spectral analysis of the time series representing average temperatures during the last ice age featuring the Dansgaard-Oeschger events reveals an a-stable noise component with an a ~ 1.78. Based on this observation, papers in the physics literature attempted a qualitative interpretation by studying diffusion equations that describe simple dynamical systems perturbed by small LÃ©vy noise. We study exit and transition problems for solutions of stochastic differential equations and stochastic reaction-diffusion equations derived from this proto type. Due to the heavy-tail nature of the a-stable component of the noise, the results differ strongly from the well known case of purely Gaussian perturbations. For SPDE, transitions are governed by the modes with the largest jumps.