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We review some of the theory relevant to passage times of one-dimensionalL\'evy processes out of bounded regions, highlighting results that are usefulin physical phenomena modelled by heavy-tailed L\'evy flights. The process ishypothesised to describe the motion of a particle on the line, starting at $0$,and exiting either a fixed interval $[-r, r]$, $r > 0$, or a time-dependent,expanding, set of intervals of the form $[-r t^\kappa, r t^\kappa]$, $r > 0$,$\kappa > 0$. Asymptotic behaviour of the exit time may be as $r \downarrow 0$or as $r \to \infty$, but particular emphasis is placed herein on "small time"approximations, corresponding to exits from or transmissions through thinstrips. Applications occur for example in the transmission of photons throughmoderately doped thin or thick wafers by means of "photon recycling", and inatmospheric radiation modelling.

Thin and Thick Strip Passage Times for L\'evy Flights and L\'evy Processes